Electronic Journal of Qualitative Theory of Differential Equations EJQTDE HU ISSN 1417-3875 http://www.math.u-szeged.hu/ejqtde/ ejqtde@server.math.u-szeged.hu 1 Research paper E. J. Qualitative Theory of Diff. Equ. <div><p class="publication_head"><b>YEAR</b></p></div> no 2 Monograph series E. J. Qualitative Theory of Diff. Equ., Monograph Series <div><p class="publication_head">Monograph Series</p> </div> yes 3 9QTDE Proceedings E. J. Qualitative Theory of Diff. Equ., Proc. 9'th Coll. Qualitative Theory of Diff. Equ. <div><p class="publication_head">Proceedings<br />of<br /><b>The 9'th Colloquium on the Qualitative Theory of Differential Equations</b><br />(June 28--July 1, 2011, Szeged, Hungary)<br />edited by: L. Hatvani, T. Krisztin and R. Vajda</p> </div> yes 4 Special Edition I E. J. Qualitative Theory of Diff. Equ., Spec. Ed. I <div><p class="publication_head">Special Edition I (2009)<br /> <b><i>Honoring the Career of John Graef<br />on the Occasion of His Sixty-Seventh Birthday</i></b><br />edited by: P. Eloe and J. Henderson</p></div> yes 5 6QTDE Proceedings E. J. Qualitative Theory of Diff. Equ., Proc. 6'th Coll. Qualitative Theory of Diff. Equ. <div><p class="publication_head">Proceedings<br />of<br /><b>The 6'th Colloquium on the Qualitative Theory of Differential Equations</b><br />(August 10--14, 1999, Szeged, Hungary)<br />edited by: G. Makay and L. Hatvani</p> </div> yes 6 7QTDE Proceedings E. J. Qualitative Theory of Diff. Equ., Proc. 7'th Coll. Qualitative Theory of Diff. Equ. <div><p class="publication_head">Proceedings<br />of<br /><b>The 7'th Colloquium on the Qualitative Theory of Differential Equations</b><br />(July 14--18, 2003, Szeged, Hungary)<br />edited by: L. Hatvani and T. Krisztin</p></div> yes 7 8QTDE Proceedings E. J. Qualitative Theory of Diff. Equ., Proc. 8'th Coll. Qualitative Theory of Diff. Equ. <div><p class="publication_head">Proceedings<br />of<br /><b>The 8'th Colloquium on the Qualitative Theory of Differential Equations</b><br />(June 25--28, 2007, Szeged, Hungary)<br />edited by: L. Hatvani and T. Krisztin</p> </div> yes 2 Professor Vajda R. ejqtde@server.math.u-szeged.hu Bolyai Institute, University of Szeged, Hungary http://www.math.u-szeged.hu/~vajda/
no no no no yes 3 Prof. Makay G. makayg@Math.u-szeged.hu Bolyai Institute, University of Szeged, Hungary http://www.math.u-szeged.hu/~makay/
no no no no no 4 Professor Artstein Z. zvi.artstein@weizmann.ac.il The Weizmann Institute of Science, Rehovot, Israel http://www.wisdom.weizmann.ac.il/~zvika/
no no no no no 5 Professor Farkas M. fm@math.bme.hu Technical University, Budapest, Hungary http://www.math.bme.hu/
no no no no no 6 Professor Furumochi T. furumochi@riko.shimane-u.ac.jp Shimane University, Matsue, Japan http://www.math.shimane-u.ac.jp/index-e.html
yes no no no no 7 Professor Graef J. R. john-graef@utc.edu University of Tennessee at Chattanooga, Chattanooga, TN, U.S.A. http://www.utc.edu/Academic/Mathematics/faculty/people.php
yes no no no no 8 Professor Haddock J. jhaddock@memphis.edu The University of Memphis, Tennessee, USA http://www.msci.memphis.edu/faculty/haddockj.html
no no no no no 10 Professor Kato J. Tohoku University, Sendai, Japan
no no no no no 11 Prof. Kiguradze I. kig@rmi.ge A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, Tbilisi, Georgia http://www.rmi.ge/~kig
ordinary differential equations, boundary value problems, oscillation theory, qualitative theory, partial differential equations, hyperbolic equations
 yes no no no no 13 Professor Lakshmikantham V. lakshmik@fit.edu Florida Institute of Technology, Melbourne, Florida, U.S.A. https://services.fit.edu/profiles/profile.php?value=149
no no no no no 14 Professor Litsyn E. elena.litsyn@weizmann.ac.il Department of Mathematics, Ben Gurion University http://www.math.bgu.ac.il/~elena/index.html
yes no no no no 16 Professor Mawhin J. jean.mawhin@uclouvain.be Catholic University of Louvain, Belgium http://www.uclouvain.be/math.html
yes no no no no 18 Professor Polacik P. polacik@math.umn.edu Comenius University, Bratislava, Slovakia http://www.iam.fmph.uniba.sk/institute/polacik/
no no no no no 19 Professor Pucci P. pucci@dmi.unipg.it University of Perugia, Italy http://www.dmi.unipg.it/~pucci/
yes no no no no 20 Professor Serrin J. B. serrin@math.umn.edu University of Minnesota, Minneapolis, U.S.A. http://www.math.umn.edu/~serrin/
no no no no no 22 Professor Walther H.-O. Hans-Otto.Walther@math.uni-giessen.de University of Giessen, Germany http://www.math.uni-giessen.de/Analysis/organisation/Walther/home_ger.htm
functional differential equations, dynamical systems
yes no no no no 23 Professor Wu J. H. wujh@mathstat.yorku.ca York University, Ontario, Canada http://www.math.yorku.ca/new/people/wuJ.html
yes no no no no 24 Professor Zanolin F. zanolin@dimi.uniud.it University of Udine, Italy http://www.dimi.uniud.it/Members/fabio.zanolin
nonlinear ordinary differential equations, periodic solutions, boundary value problems, topological methods
 yes no no no no 25 Professor Zhang Bo bzhang@uncfsu.edu Fayetteville State University, North Carolina, U.S.A. http://faculty.uncfsu.edu/bzhang/
ordinary and delay differential equations, Volterra integral equations, fractional differential equations
 yes no no no no 26 Professor Terjéki J. terjeki@math.u-szeged.hu Bolyai Institute, University of Szeged, Hungary http://www.math.u-szeged.hu/
no no no no no 27 Professor Hino Y. hino@math.s.chiba-u.ac.jp Chiba University, Chiba, Japan http://www.math.s.chiba-u.ac.jp/index-e.html
no no no no no 28 Professor Xu J. Hunan University, Changsha, P. R. China http://www.hunu.edu.cn/huda_eng.html
no no no no no 29 Professor Wang Z. zcwang@mail.hunu.edu.cn Hunan University, Changsha, P. R. China http://www.hunu.edu.cn/huda_eng.html
no no no no no 30 Professor Zheng Z. Anhui University, Hefei, P. R. China http://www.ahu.edu.cn/~jt/AHUENG.HTM
no no no no no 31 Professor Fu X. Shandong Normal University, Jinan, P. R. China http://www.sdu.edu.cn/esdu/yx/ematht.html
no no no no no 32 Professor Jiang Daqing sxxi@ivy.nenu.edu.cn Northeast Normal University, Changchun, P. R. China http://www.nenu.edu.cn/ehome.html
no no no no no 33 Professor Weng P. wengpx@scnu.edu.cn South China Normal University, Guangzhou, P. R. China http://www.scnu.edu.cn/scnuy.html
no no no no no 34 Professor Aassila M. aassila@irma.u-strasbg.fr Université Louis Pasteur et C.N.R.S., Strasbourg Cédex, France http://www.u-strasbg.fr/
no no no no no 35 Professor Knyazhishche L. B. KLB@im.bas-net.by Institute of Mathematics, National Academy of Sciences of Belarus, Belarus http://www.im.bas-net.by/
no no no no no 36 Professor Scheglov V. A. scheglov@im.bas-net.by Institute of Mathematics, National Academy of Sciences of Belarus, Belarus http://www.im.bas-net.by/
no no no no no 37 Professor Cavalcanti M. M. marcelo@gauss.dma.uem.br Universidade Estadual de Maringá, Brasil http://www.dma.uem.br/~marcelo/index.htm
no no no no no 38 Professor Cavalcanti V. N. D. valeria@gauss.dma.uem.br Universidade Estadual de Maringá, Brasil http://www.dma.uem.br/~valeria/index.htm
no no no no no 39 Professor Soriano J. A. soriano@wnet.com.br Universidade Estadual de Maringá, Brasil http://gauss.dma.uem.br/
no no no no no 40 Professor Rocha A. angela@dmm.im.ufrj.br Universidade Federal do Rio de Janeiro, Brasil http://www.dmm.im.ufrj.br/staff/rocha.html
no no no no no 41 Professor Naito T. naito@matha.e-one.uec.ac.jp University of Electro-Communications, Tokyo, Japan http://matha.e-one.uec.ac.jp/
no no no no no 42 Professor Minh N. V. minh@im.uec.ac.jp University of Electro-Communications, Tokyo, Japan http://matha.e-one.uec.ac.jp/
no no no no no 43 Professor Shin J. S. shinjs@tech.korea-u.ac.jp Korea University, Tokyo, Japan http://www.korea-u.ac.jp/
no no no no no 44 Professor Shiwang M. shiwangm@public.wh.hb.cn Huazhong University of Science and Technology, Wuhan, P. R. China http://sun200.whnet.edu.cn/enghust/enghome.htm
no no no no no 45 Professor Bayrak V. vbayrak@yildiz.edu.tr Istanbul Technical University, Istanbul, TURKEY http://www.mat.itu.edu.tr/
no no no no no 46 Professor Can M. mcan@itu.edu.tr Istanbul Technical University, Istanbul, TURKEY http://www.mat.itu.edu.tr/mcan.html
no no no no no 47 Professor Darwish Mohamed Abdalla darwishma@yahoo.com Department of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, Jeddah, Saudi Arabia
no no no no no 48 Professor Partsvania N. ninopa@rmi.ge A. Razmadze Mathematical Institute, Tbilisi, Georgia http://www.rmi.acnet.ge/~ninopa/
no no no no no 49 Professor Omari P. omari@univ.trieste.it University of Trieste, Italy http://mathsun1.univ.trieste.it/people/omari_eng.html
no no no no no 50 Professor Grossinho M. R. mrg@ptmat.lmc.fc.ul.pt Technical University of Lisboa, Portugal http://cmaf.lmc.fc.ul.pt/Members/cmaf_member.cgi?action=show_member&member_id=50
no no no no no 51 Professor Korman P. kormanp@math.uc.edu University of Cincinnati, Ohio, U.S.A. http://math.uc.edu/faculty/kormanp.htm
no no no no no 53 Professor Harris B. J. harris@math.niu.edu Northern Illinois University, DeKalb, Illinois, U.S.A. http://www.math.niu.edu/faculty/harris.html
no no no no no 54 Professor Marzano F. FMARZANO@edinboro.edu Edinboro University of Pennsylvania, Edinboro, Pennsylvania, U.S.A. http://www.edinboro.edu/cwis/Math-CS/facprof.htm#marzano
no no no no no 55 Professor Kirane M. Mokhtar.kirane@u-picardie.fr Antenne de l'Université de Picardie Jules Verne http://www.u-picardie.fr/
no no no no no 57 Professor Henderson J. johnny_henderson@baylor.edu Department of Mathematics, Baylor University, Waco, TX, U.S.A. http://www.baylor.edu/math/index.php?id=54009
boundary value problems for ordinary differential equations, boundary value problems for finite difference equations, boundary value problems for fractional differential equations
 yes no no no no 58 Professor Chyan C. J. chuanjen@mail.tku.edu.tw Tamkang University, Taipei, Taiwan http://www.tku.edu.tw/English/
no no no no no 59 Professor Guedda M. Mohamed.Guedda@u-picardie.fr Université de Picardie Jules Verne, Amiens, France http://www.u-picardie.fr/
no no no no no 64 Professor Ma T. F. matofu@dma.uem.br Universidade Estadual de Maringá, Maringá, Brazil http://www.dma.uem.br/~matofu/
no no no no no 65 Professor Gao Hongjun gaohj@hotmail.com Nanjing Normal University, Nanjing, China
Nonlinear Evolutionary Equations and stochastic PDES
 no no no no no 66 Professor Somolinos A. somolinos@mindspring.com Mercy College, Dobbs Ferry, NY, U.S.A.
no no no no no 68 Professor Nepomnyaschchikh Yu. yuvn@psu.ru Perm State University,Perm,Russia http://www.psu.ru/
no no no no no 69 Professor Ponosov A. arkadi@umb.no Norwegian University of Life Sciences, As, Norway http://www.nlh.no/imf/
no no no no no 70 Professor Ntouyas S. K. sntouyas@uoi.gr University of Ioannina, Ioannina, Greece http://www.math.uoi.gr/~sntouyas/
no no no no no 71 Professor Benchohra M. benchohra@univ-sba.dz Université de Sidi Bel Abbés, Sidi Bel Abbés, Algérie http://www-ldm.univ-sba.dz/
no no no no no 72 Professor Bognár G. matvbg@uni-miskolc.hu University of Miskolc, Miskolc-Egyetemváros, Hungary http://www.uni-miskolc.hu/
no no no no no 73 Professor Cermák J. cermak.j@fme.vutbr.cz Technical University of Brno, Brno, Czech Republic http://www.mat.fme.vutbr.cz/
no no no no no 76 Professor Dosla Z. dosla@math.muni.cz Masaryk University, Brno, Czech Republic http://www.math.muni.cz/~dosla/
no no no no no 77 Professor Dosly O. dosly@math.muni.cz Masaryk University, Brno, Czech Republic http://www.math.muni.cz/~dosly/
linear differential and difference equations and systems, half-linear differential equations
 yes no no no no 78 Professor Dragan V. Vasile.Dragan@imar.ro Institute of Mathematics of the Romanian Academy, Bucharest, Romania http://www.imar.ro/~vdragan/
no no no no no 79 Professor Feckan M. michal.feckan@fmph.uniba.sk Comenius University, Bratislava, Slovakia http://hore.dnom.fmph.uniba.sk/members/feckan.html
ordinary differential equations, partial differential equations, dynamical systems, bifurcation, chaos
 yes no no no no 81 Professor Maric V. vojam@medal.co.yu Serbian Academy of Sciences and Arts, Novi Sad, Yugoslavia
no no no no no 82 Professor Medvedeva N. medv@cgu.chel.su Chelyabinsk State University, Chelyabinsk, Russia http://www.cgu.chel.su/english/index.html
no no no no no 83 Professor Péics H. peics@gf.uns.ac.rs University of Novi Sad, Subotica, Serbia and Montenegro
no no no no no 84 Professor Rasvan V. vrasvan@automation.ucv.ro University of Craiova, Craiova, Romania
Control Theory, Differential equations with deviated argument, Oscillations, Stability
 no no no no no 87 Professor Ronto M. matronto@gold.uni-miskolc.hu University of Miskolc, Miskolc-Egyetemváros, Hungary http://www.uni-miskolc.hu/
no no no no no 88 Professor Schwabik S. schwabik@math.cas.cz Math. Inst. Acad. Sci. Czech Republic, PRAHA 1, 115 67, Czech Republic http://www.math.cas.cz/~schwabik/
no no no no no 89 Professor Srzednicki R. srzednic@im.uj.edu.pl Jagiellonian University, Krakow, Poland http://www.im.uj.edu.pl/index.en.html
no no no no no 90 Professor Stanek S. svatoslav.stanek@upol.cz Department of Mathematics, Olomouc, Czech Republic http://www.upol.cz/
BVPs for differentilal equations, fractional differential equations
 no no no no no 91 Professor Tkachenko V. vitk@imath.kiev.ua Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine http://www.imath.kiev.ua/
no no no no no 93 Professor Marini Mauro mauro.marini@unifi.it University of Florence, Firenze, Italy
no no no no no 94 Professor Cecchi M. mariella.cecchi@unifi.it University of Florence, Firenze, Italy
no no no no no 95 Professor Morozan T. tmorozan@stoilow.imar.ro Institute of Mathematics of the Romanian Academy, Bucharest, Romania http://www.imar.ro/~tmorozan/
no no no no no 96 Professor Ionita A. ionita@aero.incas.ro Institute of Theoretical and Experimental Analisys of Aeronautical Structures, Bucharest, Romania http://www.incas.ro/
no no no no no 97 Professor Marik Robert marik@mendelu.cz Mendel University in Brno, Brno, Czech Republic http://user.mendelu.cz/marik
no no no no no 98 Professor Batcheva E. Chelyabinsk State University, Chelyabinsk, Russia http://www.cgu.chel.su/english/index.html
no no no no no 99 Professor Danciu D. University of Craiova, Craiova, Romania
no no no no no 103 Professor Zubrinic D. darko.zubrinic@fer.hr University of Zagreb, Zagreb, Croatia
no no no no no 104 Professor Zhang Z. Hunan University, Changsha, P. R. China http://www.hunu.edu.cn/huda_eng.html
no no no no no 105 Professor Yu J. Hunan University, Changsha, P. R. China http://www.hunu.edu.cn/huda_eng.html
no no no no no 107 Professor Eloe P. peloe1@udayton.edu University of Dayton, Dayton, Ohio, U.S.A. http://homepages.udayton.edu/~eloe/
boundary value problems, fractional differential and difference equations, ordinary and delay differential equations
 yes no no no no 108 Professor Elbert Á. elbert@renyi.hu Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary http://www.renyi.hu/
no no no no no 109 Professor Atkinson F. V. 217 Chaplin Crescent, Toronto, Ontario, Canada
no no no no no 110 Professor Georgiev S. sgg2000bg@yahoo.com University of Sofia, Sofia, Bulgaria
no no no no no 113 Professor Raffoul Y. Youssef.Raffoul@notes.udayton.edu University of Dayton, Dayton, OH, U.S.A. http://academic.udayton.edu/YoussefRaffoul/
no no no no no 114 Professor Islam M. muhammad.islam@notes.udayton.edu University of Dayton, Dayton, U.S.A. http://homepages.udayton.edu/~islam/
no no no no no 117 Professor Weikard R. rudi@vorteb.math.uab.edu University of Alabama, Birmingham, Alabama, U.S.A. http://www.math.uab.edu/rudi/
no no no no no 121 Professor Saker S. H. shsaker@mans.edu.eg Mansoura University, Mansoura, Egypt http://www.mans.eun.eg/
Ordinary and functional differential equations (delay and neutral delay equations), Difference equations, Nonlinear dynamical systems, Mathematical models in Biology, Ecology, Economy, Epidemiology, and Medicine, etc.
Dynamic equations on time scales, dynamic inequalities on time scales, Applications of opial and Wirtinger inequalities on the zeros of Riemann Zeta Function.

 no no no no no 122 Professor Hegedûs J. hegedusj@math.u-szeged.hu Bolyai Institute, Szeged, Hungary http://www.math.u-szeged.hu/
no no no no no 123 Professor Karsai J. karsai@dmi.u-szeged.hu University of Szeged, Szeged, Hungary www.model.u-szeged.hu
no no no no no 124 Professor Krisztin T. krisztin@math.u-szeged.hu Bolyai Institute, Szeged, Hungary http://www.math.u-szeged.hu/~krisztin
yes no no no no 125 Professor Fabry C. fabry@mail.math.ucl.ac.be Catholic University of Louvain, Belgium http://www.math.ucl.ac.be/
no no no no no 126 Professor Yanagida E. yanagida@ms.u-tokyo.ac.jp University of Tokyo, Japan http://www.ms.u-tokyo.ac.jp/
no no no no no 127 Professor Goltser Ya. The College of Judea and Samaria, Ariel, Israel http://www.yosh.ac.il/
no no no no no 128 Professor Feng Z. zsfeng@math.tamu.edu Texas A&M University, College Station, TX, U.S.A. http://www.math.tamu.edu/
no no no no no 129 Professor Gadam S. 'Yashodha', Chitradurga, India
no no no no no 130 Professor Iaia J. A. iaia@unt.edu University of North Texas, TX, U.S.A. http://www.math.unt.edu/~iaia/
no no no no no 132 Professor Santos M. L. ls@ufpa.br UFPA, Para, Brazil http://www.ufpa.br/
Partial Differential Equations and applications.
 no no no no no 134 Professor Yin Jingxue yjx@scnu.edu.cn South China Normal University, Guangzhou, P. R. China
no no no no no 135 Professor Liu Changchun liucc@jlu.edu.cn Jilin University, Changchun, P. R. China http://www.jlu.edu.cn/
no no no no no 137 Professor Khukhunashvili Z. V. amareyah@gol.ge Tbilisi State University, Tbilisi, Georgia
no no no no no 138 Professor Khukhunashvili Z. Z. zviad.khukhunashvili@tougaloo.edu Tougaloo College, Tougaloo, U.S.A.
no no no no no 141 Professor Lin Z. zglin68@hotmail.com Yangzhou University, Yangzhou, China
no no no no no 143 Professor Kouachi S. kouachi.said@caramail.com Central University of Tebessa, Algeria
no no no no no 148 Professor El Hachimi A. aelhachi@yahoo.fr UFR Mathématiques Appliquées et Industrielles, El Jadida, Maroc
no no no no no 149 Professor El Ouardi H. h.elouardi@ensem.ac.ma E.N.S.E.M, Maroc http://www.ucd.ac.ma/
no no no no no 150 Associate Professor Vanualailai Jito vanualailai@usp.ac.fj University of the South Pacific, Suva, FIJI http://www.scims.fste.usp.ac.fj/index.php?id=5162
Stability of Nonlinear Systems; Artificial Neural Networks, Volterra Integro-differential Systems, Planning Algorithms, and Internet Congestion Control (new)

Volterra Integro-differential Systems

These have their roots in biological growth problems, whose origins can be traced from the Malthusian model through the logistic equation, the predator-prey system of Lotka and Volterra and Volterra's own formulation of integral equations regarding age distribution in population.

Artificial Neural Networks

ANNs are crude mathematical models of biological neural systems. They have to be designed in such a way that their synaptic weights, which are the strengths of signals or communications between neurons, could effectively store and
retrieve memories.

Planning Algorithms

In robotics, motion planning is an important component. The focus is on designing algorithms that generate useful motions by processing complicated geometric models.

Swarm Intelligence

Swarming, or aggregations of organisms in groups, can be found in nature in many organisms ranging from simple bacteria to mammals. A relatively new area of research looks into the behavior of swarms, in particular to how a swarm's collective behavior could be mimicked to solve challenging engineering problems.

Internet Congestion Control (new area of interest)

One of the most recent and exciting areas of research in the stability analysis of systems deals with the need to control traffic in the ever-growing Internet in a more systematic, rigorous and efficient manner.
no no no no no 152 Professor Chouikha R. A. chouikha@math.univ-paris13.fr University of Paris, Paris, France http://www.univ-paris13.fr/
no no no no no 154 Professor Anane A. anane@sciences.univ-oujda.ac.ma University Mohamed Ist, Oujda, Morocco http://www.univ-oujda.ac.ma/
no no no no no 156 Professor Moussa M. mohammed.moussa@caramail.com University Ibn Tofail, Kenitra, Morocco
no no no no no 157 Professor Simon P. simonp@cs.elte.hu Eötvös Loránd University, Budapest, Hungary
no no no no no 158 Professor Hofbauer J. josef.hofbauer@univie.ac.at University of Vienna, Vienna, Austria http://mailbox.univie.ac.at/Josef.Hofbauer/
no no no no no 159 Professor Li Yongkun yklie@ynu.edu.cn Yunnan University, Kunming, Yunnan, P. R. China
no no no no no 163 Professor Clark H. hclark@vm.uff.br Universidade Federal Fluminense, Niteroi-RJ, Brazil
no no no no no 164 Professor Mazouzi Said mazouzi_sa@yahoo.fr Badji Mokhtar-Annaba University, Algeria http://www.univ-annaba.org/
Fractional order differential equations, integral inequalities
 no no no no no 168 Professor Hristova S.G. sgh2222@louisiana.edu University of Louisiana at Lafayette, Lafayette, U.S.A.
no no no no no 170 Professor Avramescu C. zarce@central.ucv.ro University of Craiova, Craiova, Romania
no no no no no 171 Professor Vladimirescu C. vladimirescucris@yahoo.com University of Craiova, Craiova, Romania
no no no no no 172 Professor Ouahab A. agh_ouahab@yahoo.fr Université de Sidi Bel Abbés, Sidi Bel Abbés, Algérie http://www-ldm.univ-sba.dz/
Impulsive differential equations and inclusions, fractional differential equations and inclusions, solutions sets, fixed point theory and applications.
 no no no no no 174 Professor Hajji A. hajid2@yahoo.fr Departement of Mathematics And Informatics, Rabat, Morocco
no no no no no 175 Professor Hanebaly E. hanebaly@fsr.ac.ma Departement of Mathematics And Informatics, Rabat, Morocco
no no no no no 178 Professor Valls C. cvalls@math.ist.utl.pt Instituto Superior Técnico, Lisboa, Portugal
no no no no no 179 Professor Benkirane A. abd.benkirane@gmail.com Department of Mathematics, University Sidi Mohamed Ben Abdellah, Fez, Morocco
no no no no no 180 Professor Aharouch L. l_aharouch@yahoo.fr Department of Mathematics, Faculty of Sciences of Fez, Fez, Morocco
no no no no no 181 Professor Azroul E. azroul_elhoussine@yahoo.fr Department of Mathematics, Faculty of Sciences of Fez, Fez, Morocco
no no no no no 186 Professor El Khalil A. lkhlil@hotmail.com 3-1390, Boul. Décaire Montreal (Qc) H4L 3N1, Canada
no no no no no 187 Professor Ouanan M. m_ouanan@hotmail.com Dhar-Mahraz, Atlas-Fes, Fes, Morocco
no no no no no 188 Professor Touzani A. atouzani@iam.net.ma Dhar-Mahraz, Atlas-Fes, Fes, Morocco
no no no no no 189 Professor Wang Yifu wangyifu@bit.edu.cn Beijing Institute of Technology, Beijing, P. R. China
no no no no no 190 Professor Meng Y. Beijing Institute of Technology, Beijing, P.R. China
no no no no no 192 Professor Tsamatos P. Ch. ptsamato@cc.uoi.gr University of Ioannina, Ioannina, Greece
no no no no no 196 Professor Riahi L. Lofti.Riahi@fstn.rnu.tn Campus Universitaire, Tunis, Tunisia
no no no no no 198 Professor Teramoto T. teramoto@math.sci.hiroshima-u.ac.jp Hiroshima University, Higasi-Hiroshima, Japan
no no no no no 204 Professor Han Yuzhu hanyuzhu2003@yahoo.cn Jilin University, Changchun, P. R. China
no no no no no 205 Professor Aibeche A. aibeche@wissal.dz Universite Ferhat Abbes, Setif, Algeria
no no no no no 206 Professor Shao Z. Zhoude.Shao@millersville.edu Millersville University, Millersville, U.S.A.
no no no no no 207 Professor Lu Y. ylu@bloomu.edu Bloomsburg University, Bloomsburg, U.S.A.
no no no no no 212 Professor Lei Yutian leiyutian@njnu.edu.cn Department of Mathematics, Nanjing Normal University, Nanjing, China
no no no no no 215 Professor Chate D. N. Kasubai, Gurucul Colony, Maharashtra, India
no no no no no 217 Professor Ben Yousif N. M. nuri_mofideh@math.u-szeged.hu Tripoli, Libya, Alfateh University, Department of Mathematics
no no no no no 218 Professor Menezes S. B. silvano@ufpa.br UFPa, Belém, Brasil
no no no no no 219 Professor Limaco J. Universidade Federal Fluminense, Niteroi-RJ, Brazil
no no no no no 220 Professor Medeiros L. A. lmedeiros@abc.org.br UFRJ, Rio de Janeiro, Brasil
no no no no no 221 Professor Khan Rahmat Ali rahmat_alipk@yahoo.com University of Malakand, Chakdara Dir(L), Khyber Pukhtunkhwa, Pakistan
Boundary Value problems for differential equations, Nonlinear Analysis
 no no no no no 222 Professor Georgieva P. p_g@abv.bg University of Sofia, Sofia, Bulgaria
no no no no no 223 Professor Appleby J. A. D. john.appleby@dcu.ie School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland http://webpages.dcu.ie/~applebyj
no no no no no 224 Professor Reynolds D. W. david.reynolds@dcu.ie CMDE, School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland http://webpages.dcu.ie/~reynoldd
no no no no no 225 Professor Faria T. tfaria@ptmat.fc.ul.pt Universidade de Lisboa, Lisboa, Portugal http://cmaf.lmc.fc.ul.pt/membros/linha7/teresafaria-pt.html
no no no no no 226 Professor Tvrdy M. tvrdy@math.cas.cz Mathematical Institute, Academy of Sciences of the Czech Republic, Prague, Czech Republic http://www.math.cas.cz/~tvrdy
no no no no no 228 Professor Hartung F. hartung@szt.vein.hu Department of Mathematics and Computing, University of Veszprém, Veszprém, Hungary http://www.szt.vein.hu/~hartung
no no no no no 229 Professor Gyõri I. gyori@almos.vein.hu Department of Mathematics and Computing, University of Pannonina, Veszprém, Hungary http://www.szt.vein.hu/~gyori/
no no no no no 230 Professor Kaufmann E. erkaufmann@ualr.edu University of Arkansas at Little Rock, Little Rock, AR, U.S.A.
no no no no no 231 Professor Ungureanu V. M. vio@utgjiu.ro Constantin Brancusi University, Targu-Jiu, Romania
stochastic stability and stochastic optimal control
 no no no no no 232 Professor Shchobak N. natalja_shch@rambler.ru Mathematical Faculty, Uzhgorod National University, Ukraine
no no no no no 234 Professor Ezzinbi K. ezzinbi@ucam.ac.ma Université Cadi Ayyad, Marrakech, Morocco
Dynamical systems
Partial functional differential equations
Evolution equations
Delay and ordinary differential equations

 no no no no no 235 Professor Jazar M. mjazar@ul.edu.lb Département de Mathématiques, Université Libanaise, Beyrouth, Liban
no no no no no 236 Professor Mavridis K. G. kmavride@otenet.gr University of Ioannina, Ioannina, Greece
no no no no no 237 Professor Kosmatov N. nxkosmatov@ualr.edu University of Arkansas at Little Rock, Little Rock, AR, U.S.A.
ordinary differential equations, dynamic equations on time scales
 yes no no no no 238 Professor Mackey D. dana.mackey@dcu.ie CMDE, School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland http://webpages.dcu.ie/~mackeyd
no no no no no 239 Professor Giorgi T. tgiorgi@nmsu.edu New Mexico State University, Las Cruces, U.S.A.
no no no no no 240 Professor O'Leary M. moleary@towson.edu Towson University, Towson, U.S.A.
no no no no no 241 Professor Yang Bo byang@kennesaw.edu Kennesaw State University, Kennesaw, GA, U.S.A.
no no no no no 242 Professor Qian Chuanxi Mississippi State University, Mississippi, U.S.A.
no no no no no 243 Professor Savithri R. Peryiar University, Salem 636011, Tamilnadu, India
no no no no no 244 Professor Thandapani E. ethandapani@yahoo.co.in Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India
no no no no no 245 Professor Halmschlager A. andhalm@math.bme.hu Budapest University of Technology and Economics, Budapest , Hungary
no no no no no 246 Professor Szenthe L. Budapest University of Technology and Economics, Budapest , Hungary
no no no no no 247 Professor Tóth J. jtoth@math.bme.hu Budapest University of Technology and Economics, Budapest , Hungary
no no no no no 248 Professor Horváth Bokor R. hrozsa@almos.vein.hu University of Veszprém, Veszprém, Hungary
no no no no no 249 Professor Lomtatidze A. bacho@math.muni.cz Institute of Mathematics, Academy of Sciences of the Czech Republic
no no no no no 250 Professor Oplustil Z. oplustil@fme.vutbr.cz Brno University of Technology, Brno, Czech Republic
no no no no no 251 Professor Popescu D. dpopescu@automation.ucv.ro University of Craiova, Craiova, Romania
no no no no no 252 Professor Stefan R. stefan@ricatti.pub.ro University "Politehnica", Bucharest, Romania
no no no no no 253 Professor Rózsa Z. rozsaz@chardonnay.math.bme.hu Budapest University of Technology and Economics, Budapest , Hungary
no no no no no 254 Professor Simon L. simonl@ludens.elte.hu L. Eötvös University, Budapest, Hungary
partial differential equations
 yes no no no no 255 Professor Sidi Ammi M. R. sidiammi@hotmail.com University Chouaib Doukkali, El Jadida, Maroc http://www.ucd.ac.ma/
no no no no no 257 Professor Langlais M. langlais@sm.u-bordeaux2.fr University Victor Segalen, Bordeaux, France
no no no no no 258 Professor Ramirez S. M. soramire@hotmail.com Richard J. Daley College, Chicago, U.S.A.
no no no no no 259 Professor Rocha M. P. C. UFPA, Para, Brazil http://www.ufpa.br/
no no no no no 260 Professor Pereira D. C. UFPA, Para, Brazil http://www.ufpa.br/
no no no no no 261 Professor Ferreira J. UFPA, Para, Brazil http://www.ufpa.br/
no no no no no 262 Professor Stepankova H. stepanh@pf.jcu.cz University of South Bohemia, Ceske Budejovice, Czech Republic
no no no no no 263 Professor Xu Zhiting xuzhit@126.com South China Normal University, Guangzhou, P. R. China
no no no no no 264 Professor Devin S. siobhan.devin2@mail.dcu.ie CMDE, School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland
no no no no no 265 dr Tomecek Jan jan.tomecek@upol.cz Palacky University, Olomouc, Czech Republic
impulsive ODE, singular ODE
 no no no no no 266 dr Guillaume S. sophie.guillaume@univ-avignon.fr University of Avignon, Avignon, France
no no no no no 267 Professor Syam A. syam@fstg-marrakech.ac.ma Cadi Ayyad University, Marrakech, Marocco
no no no no no 268 Professor Belarbi A. aek_belarbi@yahoo.fr Université de Sidi Bel Abbés, Sidi Bel Abbés, Algérie http://www-ldm.univ-sba.dz/
no no no no no 269 Professor Fisnarova Simona fisnarov@mendelu.cz Mendel University in Brno, Brno, Czech Republic
no no no no no 270 Professor Vera Octavio Paulo Villagran overa@ubiobio.cl Universidad del Bío-Bío, Concepción, Chile
Partial Differential Equations
 no no no no no 271 Professor Kozakevicius A. alicek@smail.ufsm.br Universidade Federal de Santa Maria, Santa Maria, Brasil
no no no no no 273 Professor Nobles J. jwnobles@ualr.edu University of Arkansas at Little Rock, Little Rock, USA
no no no no no 274 Professor Karna B. karna@marshall.edu Marshall University, West Virginia, USA
no no no no no 275 Professor Mishev D. dimichev@pvamu.edu Prairie View A&M University, Prairie View, USA
no no no no no 276 Professor Dimitrova M. B. mbdimitrova@abv.bg Technical University of Sliven, Sliven, Bulgaria
no no no no no 277 Professor Pumarino A. apv@pinon.ccu.uniovi.es Universidad de Oviedo, Oviedo, Spain
no no no no no 278 Professor Calahorrano M. calahor@server.epn.edu.ec Escuela Politécnica Nacional, Departamento de Mathemática, Quito, Ecuador http://www.math.epn.edu.ec/miembros/calahorrano.htm
no no no no no 279 Professor Mena H. hmena@server.epn.edu.ec Escuela Politécnica Nacional, Departamento de Mathemática, Quito, Ecuador http://www.math.epn.edu.ec/~hmena
no no no no no 280 Professor Correa F. J. S. A. fjsacorrea@gmail.com UFPa, Belém, Brasil
no no no no no 281 Professor Pinter G. gapinter@uwm.edu University of Wisconsin-Milwaukee, Milwaukee, U.S.A. http://www.uwm.edu/~gapinter/
partial differential equations, mathematical biology, population dynamics
 yes no no no no 282 Professor Alvarez Samaniego B. balvarez@impa.br IMECC-UNICAMP, Campinas, Brasil
no no no no no 283 Professor Hopkins Britney bhopkins3@uco.edu University of Central Oklahoma, OK, U.S.A.
Differential Equations
 no no no no no 284 Professor Karande B. D. Kasubai, Gurucul Colony, Maharashtra, India
no no no no no 285 Professor Melkemi L. lmekmi@yahoo.fr University of Batna, Batna, Algeria
no no no no no 286 Professor Mokrane A. Z. ahmed_mokr@hotmail.com University of Batna, Batna, Algeria
no no no no no 287 Professor Youkana A. youkana_amar@yahoo.fr University of Batna, Batna, Algeria
no no no no no 288 Professor Yankson E. ernestoyank@yahoo.com University of Cape Coast, Cape Coast, Ghana
no no no no no 289 Professor Amster P. pamster@dm.uba.ar Universidad de Buenos Aires, Buenos Aires, Argentina
no no no no no 290 Professor De Nápoli P. pdenapo@dm.uba.ar Universidad de Buenos Aires, Buenos Aires, Argentina
no no no no no 293 Professor Wang Chunpeng Jilin Univ., P. R. China
no no no no no 294 Professor Li Yinghua yinghua@scnu.edu.cn South China Normal University, Guangzhou, P. R. China
no no no no no 295 Professor Kwong Man Kam mankwong@polyu.edu.hk Hong Kong Polytechnic University, Hong Kong, SAR, China
no no no no no 296 Professor Boucherif A. aboucher@kfupm.edu.sa King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
no no no no no 297 Professor Bartusek M. bartusek@math.muni.cz Masaryk University, Brno, Czech Republic
ordinary differential equations
 no no no no no 298 Professor Palimkar D. S. Kasubai, Gurucul Colony, Maharashtra, India
no no no no no 299 Professor Feng Meiqiang meiqiangfeng@sina.com Beijing Institute of Technology, Beijing, P. R. China
no no no no no 300 Professor Ge Weigao gew@bit.edu.cn Beijing Institute of Technology, Beijing, P. R. China
no no no no no 301 Professor Zhang Xuemei zxm74@sina.com North China Electric Power University, Beijing, P. R. China
no no no no no 302 Dr. Becker Leigh C lbecker@cbu.edu Christian Brothers University, Memphis, TN, U.S.A. http://www.cbu.edu/~lbecker
Integral equations; integro-differential equations
 no no no no no 303 Professor Gal C. cgal@morgan.edu Morgan State University, Baltimore, MD, U.S.A.
no no no no no 304 Prof. Purnaras Ioannis C ipurnara@uoi.gr University of Ioannina, Ioannina, Greece
fractional differential equations, boundary value problems, stability, difference equations, Volterra integral equations
 yes no no no no 305 Professor Baklouti H. h_baklouti@yahoo.com University of Sfax, Sfax, Tunisia
no no no no no 306 Professor Mnif M. maher.mnif@ipeis.rnu.tn University of Sfax, Sfax, Tunisia
no no no no no 307 Professor Ahmad Bashir bashirahmad_qau@yahoo.com King Abdulaziz University, Jeddah, Saudi Arabia
Boundary value problems
 no no no no no 308 Professor Alsaedi A. aalsaedi@hotmail.com King Abdulaziz University, Jeddah, Saudi Arabia
no no no no no 309 Dr Guedda Lahcene lahcene_guedda@yahoo.fr University of Tiaret, Tiaret, Algeria
no no no no no 311 Professor Abd El-Salam Sh. A. shrnahmed@maktoob.com Alexandria University, Alexandria, Egypt
no no no no no 312 Professor El-Sayed A. M. A. amasayed@hotmail.com Alexandria University, Alexandria, Egypt
no no no no no 313 Professor Maroun M. maroun@ulm.edu University of Louisiana at Monroe, Monroe, LA, U.S.A.
no no no no no 314 Professor Pekárková E. pekarkov@math.muni.cz Masaryk University, Brno, Czech Republic
no no no no no 315 Professor Ait A. aitalifr@yahoo.fr University Hassan II-Mohammedia, Mohammedia, Morocco
no no no no no 316 Professor Sajid S. saidsajid@hotmail.com University Hassan II-Mohammedia, Mohammedia, Morocco
no no no no no 317 Professor Cernea A. acernea@fmi.unibuc.ro University of Bucharest, Bucharest, Romania
differential inclusions, optimal control
 no no no no no 318 Professor Long Shujun longer207@yahoo.com.cn (1) Leshan Teachers College, Leshan, P. R. China; (2) Sichuan University, Chengdu, P. R. China
qualitative theory of impulsive and stochastic systems, delay differential systems and neural networks
 no no no no no 319 Professor Xu Daoyi daoyixucn@yahoo.com Sichuan University, Chengdu, P. R. China
no no no no no 320 Professor Zhu Wei Sichuan University, Chengdu, P. R. China
no no no no no 321 Professor Soares U. R. UFPA, Para, Brazil http://www.ufpa.br/
no no no no no 322 Professor Anderson Douglas R. andersod@cord.edu Concordia College, Moorhead, MN, U.S.A. http://www.cord.edu/faculty/andersod/
Differential equations, difference equations, q-difference equations, dynamic equations and inequalities on time scales, discrete dynamical systems, integral inequalities, asymptotic analysis, and boundary value problems.
 no no no no no 323 Professor Moats L. M. lmmoats@cord.edu Concordia College, Moorhead, MN, U.S.A.
no no no no no 325 Professor Merazga N. nabilmerazga@yahoo.fr Centre Universitaire Larbi Ben M'hidi, Oum El Bouaghi, Algeria
no no no no no 326 Professor Hamani S. hamani_samira@yahoo.fr Université de Sidi Bel Abbés, Sidi Bel Abbés, Algérie
no no no no no 327 Professor Sheng Qin Qin_Sheng@baylor.edu Baylor University, Waco, Texas, U.S.A. http://www3.baylor.edu/~Qin_Sheng/
no no no no no 328 Professor Boukhamla R. University of Souk-Ahras, Souk-Ahras, Algeria.
no no no no no 330 Professor Wong James S. W. jsww@chinneyhonkwok.com The University of Hong Kong, City University of Hong Kong and Chinney Investment Ltd., Hong Kong
no no no no no 331 Professor Yang Liu Hefei Teacher's College, Hefei Anhui Province, P. R. China
no no no no no 332 Professor Shen Chunfang shencf2003@163.com Hefei Teacher's College, Hefei Anhui Province, P. R. China
no no no no no 333 Professor Liu Xiping xipingliu@163.com University of Shanghai for Science and Technology, Shanghai, P. R. China
no no no no no 334 Professor Redwane H. redwane_hicham@yahoo.fr Université Hassan 1, Settat, Morocco
no no no no no 335 Professor Elabbasy E. M. emelabbasy@mans.edu.eg Mansoura University, Mansoura, Egypt
no no no no no 336 Professor Elhaddad W. W. Mansoura University, Mansoura, Egypt
no no no no no 337 Professor Lawrence B. lawrence@marshall.edu Marshall University, West Virginia, USA
no no no no no 338 Professor Jamea A. a.jamea@yahoo.fr University Chouaib Doukkali, El Jadida, Maroc http://www.ucd.ac.ma/
no no no no no 339 Professor Cherkas L. cherkas@inp.by Belorussian State University of Informatics and Radioelectronics, Minsk, Belarus
no no no no no 340 Professor Grin A. grin@grsu.by Grodno State University, Grodno, Belarus
no no no no no 341 Professor Schneider K. R. schneider@wias-berlin.de Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
Qualitative Theory of ordinary differential equations, Mathematical Biology
 no no no no no 342 Professor Zhidkov P. zhidkov@thsun1.jinr.ru Bogoliubov Laboratory of Theoretical Physics, Dubna, Russia
no no no no no 344 Professor El-Shahed M. elshahedm@yahoo.com Qassim University, Qassim, Saudi Arabia
no no no no no 345 Professor Mboumi E. exmboumi@ualr.edu University of Arkansas at Little Rock, Little Rock, USA
no no no no no 346 Professor Bahuguna D. dhiren@iitk.ac.in Indian Institute of Technology, Kanpur, India
no no no no no 348 Professor Severo Uberlandio B. uberlandio@mat.ufpb.br UFPB, Paraíba, Brazil
no no no no no 349 Professor El-Morshedy Hassan A. elmorshedy@yahoo.com Abha Teachers' College, Abha, Saudi Arabia
no no no no no 350 Professor Elmatary B. M. bassantmarof@yahoo.com Mansoura University, New Damietta, Egypt
no no no no no 351 Professor Bai Chuanzhi czbai8@sohu.com Huaiyin Normal University, Huaian, Jiangsu, P. R. China
Nonlinear Functional Analysis, Ordinary Differential Equation
 no no no no no 352 Professor Xie Dapeng xiedapeng9@yahoo.com.cn Hefei Normal University, Hefei, Anhui, P. R. China
no no no no no 353 Professor Liu Yang Hefei Normal University, Hefei, Anhui, P. R. China
no no no no no 354 Professor Wang Chunli Yanbian University, Yanji, Jilin, P. R. China
no no no no no 355 Professor Hallouz A. ahmedhallouz@yahoo.fr University of Tiaret, Tiaret, Algeria
no no no no no 356 Professor Bellale S. S. Kasubai, Gurukul Colony, Maharashtra, India
no no no no no 357 Professor Tripathy A. K. arun_tripathy70@rediffmail.com Kakatiya Institute of Technology and Science, Warangal, India
no no no no no 359 Professor, Dr. Marinho A. O. alexmaiver@hotmail.com UFPI-Universidade Federal do Piauí, Parnaíba-Piauí, Brasil
Control Theory, Problems in Banach Space.
 no no no no no 360 Professor Louredo A. T. aldotl@bol.com.br UEPB, Paraíba, Brasil
no no no no no 361 Professor Lima O. A. osmundo@hs24.com.br UEPB, Paraíba, Brasil
no no no no no 362 Professor Palamides P. K. ppalam@otenet.gr Naval Academy of Greece, Piraeus, Greece http://ux.snd.edu.gr/\symbol{126}maths-ii/pagepala.htm
no no no no no 363 Professor Palamides A. P. palamid@uop.gr University of Peloponesse, Tripolis, Greece.
no no no no no 364 Professor Benhamidouche N. benhamidouche@yahoo.fr University of M'sila, M'sila, Algeria
Partial differential equations - self similar solutions
no no no no no 365 Professor El-Maghrabi E. M. esam_mh@yahoo.com Benha University, Benha, Egypt
no no no no no 366 Professor Gil' M. I. gilmi@cs.bgu.ac.il Ben Gurion University of the Negev, Beer-Sheva, Israel
no no no no no 367 Professor Liang Ruixi liangruixi123@yahoo.com.cn Central South University, Changsha, Hunan, P. R. China
Impulsive differential equation, boundary value problem
 no no no no no 368 Professor Peng Jun Central South University, Changsha, Hunan, P. R. China
no no no no no 369 Professor Shen Jianhua College of Huaihua, Huaihua, Hunan, P. R. China
no no no no no 370 Professor Dix J. G. jd01@txstate.edu Texas State University, San Marcos, Texas, U.S.A
no no no no no 371 Professor Misra N. niyatimath@yahoo.co.in Berhampur University, Berhampur, Orissa, India
no no no no no 372 Professor Padhy L. N. ln_padhy_2006@yahoo.co.in K.I.S.T., Bhubaneswar, Orissa, India
no no no no no 373 Professor Rath R. N. radhanathmath@yahoo.co.in Veer Surendra Sai University of Technology, Orissa, India
no no no no no 374 Professor Pudipeddi S. sridevi.pudipeddi@gmail.com Augsburg College, Minneapolis, MN, U.S.A.
no no no no no 376 Professor Cieutat P. Philippe.Cieutat@math.uvsq.fr Université Versailles-Saint-Quentin-en-Yvelines, Versailles cedex, France
no no no no no 377 Professor Fatajou S. fatajou@yahoo.fr Université de Cadi Ayyad, Marrakech, Morocco
no no no no no 378 Professor N'Guérékata G. M. Gaston.N'Guerekata@morgan.edu Morgan State University, E. Cold Spring Lane, Baltimore, MD, U.S.A.
no no no no no 379 Professor Hong Shihuang hongshh@hotmail.com Hangzhou Dianzi University, Hangzhou, P. R. China
no no no no no 380 Professor Qiu Zeyong qzy@hdu.edu.cn Hangzhou Dianzi University, Hangzhou, P. R. China
no no no no no 381 Professor Bartha M. bartham@math.u-szeged.hu Bolyai Institute, University of Szeged, Hungary
no no no no no 382 Professor Besenyei Á. badam@cs.elte.hu L. Eötvös University, Budapest, Hungary
no no no no no 383 Professor Dénes Attila denesa@math.u-szeged.hu Bolyai Institute, University of Szeged, Hungary http://www.math.u-szeged.hu/~denesa/
no no no no no 384 Professor Faragó I. faragois@cs.elte.hu L. Eötvös University, Budapest, Hungary
numerical methods of differential equations, numerical linear algebra, splitting methods
 no no no no no 385 Professor Horváth R. rhorvath@ktk.nyme.hu University of West-Hungary, Sopron, Hungary
no no no no no 386 Professor Hadeler K. P. hadeler@uni-tuebingen.de Arizona State University Tempe, AZ, U.S.A.
no no no no no 387 Professor Lackova D. dasa.lackova@tuke.sk Technical University of Kosice, Kosice, Slovakia
no no no no no 389 Professor Patikova Z. patikova@fai.utb.cz Tomas Bata University in Zlín, Zlín, Czech Republic
no no no no no 390 Professor Rezounenko Alexander rezounenko@univer.kharkov.ua Kharkov University, Kharkov, Ukraine http://matan.univer.kharkov.ua/avrezoun.htm
no no no no no 391 Associate Professor Gritsans Armands arminge@inbox.lv Daugavpils University, Daugavpils, Latvia http://www.de.dau.lv/mrc/ag.htm
Nonlinear boundary problems for ordinary differential equations, asymmetric problems, qualitative behavior of solutions of nonlinear differential equations, differential-geometric structures on manifolds
 no no no no no 392 Professor Sadyrbaev F. felix@latnet.lv Daugavpils University, Daugavpils, Latvia
no no no no no 393 Professor Sergejeva N. natalijasergejeva@inbox.lv Daugavpils University, Daugavpils, Latvia
no no no no no 394 Professor Pascoletti A. anna.pascoletti@dimi.uniud.it University of Udine, Italy http://www.dimi.uniud.it/
no no no no no 395 Professor Pireddu M. marina.pireddu@dimi.uniud.it University of Udine, Italy http://www.dimi.uniud.it/
no no no no no 397 Professor Kadiev R. I. dgu@dgu.ru Dagestan Scientific Center, Russian Academy of Sciences, Makhachkala, Russia
no no no no no 398 Professor Hashem H. H. G. hendhghashem@yahoo.com Alexandria University, Alexandria, Egypt
Quadratic integral equations, Functional Equations, Integral and differential equations in Banach space, Fractional Calculus, Coupled System.
 no no no no no 400 Professor Guan Wen wangdb@lut.cn Lanzhou University of Technology, Lanzhou, Gansu, P. R. China
no no no no no 401 Professor Muslim M. malikiisc@gmail.com Indian Institute of Science, Bangalore, India
Fractional Differential Equations, Applications of Semigroups Theory to Abstract Differential Equations, Inverse Problems and Control Problems.
 no no no no no 402 Professor Dahmani Zoubir zzdahmani@yahoo.fr Mostaganem University, Mostaganem, Algeria
Evolution equations, Inequality theorey, Fractional Differential equations, Fractional calculus, Numerical analysis and applied amthematics.
 no no no no no 403 Professor Mesmoudi M. M. mesmoudi@ac-creteil.fr IUFM, University Paris 12, Creteil, France
no no no no no 404 Professor Bebbouchi R. rbebbouchi@hotmail.com Houari Boumedienne University of Sciences and Technology, Algiers, Algeria
no no no no no 405 Professor Milosevic J. jefimija79@gmail.com University of Nis, Nis, Serbia and Montenegro http://www.pmf.ni.ac.yu
no no no no no 406 Professor Araruna F. D. fagner@mat.ufpb.br Universidade Federal da Paraíba, PB, Brasil
no no no no no 407 Professor Borges J. E. S. dudusampaioborges@hotmail.com Universidade Federal da Paraíba, PB, Brasil
no no no no no 408 Dr. Baghli-Bendimerad Selma selma_baghli@yahoo.fr Université de Sidi Bel Abbés, Sidi Bel Abbés, Algérie http://www-ldm.univ-sba.dz/
no no no no no 409 Professor Bezandry P. pbezandry@howard.edu Howard University, Washington, DC, U.S.A.
no no no no no 410 Professor Azzam-Laouir D. laouir.dalila@gmail.com Université de Jijel, Jijel, Algérie
differential inclusions, differential equations, optimal control
 no no no no no 411 Professor Huang M. huangmugen@yahoo.cn Hanshan Normal University, Chaozhou, P. R. China
no no no no no 412 Professor Feng W. wsy@scnu.edu.cn South China Normal University, Guangzhou, P. R. China
no no no no no 414 Professor Webb J. R. L. jeffrey.webb@glasgow.ac.uk School of Mathematics and Statistics, University of Glasgow, Glasgow, UK http://www.maths.gla.ac.uk/~jrlw/
boundary value problems for ordinary differential equations, nonlinear operators, degree theory
 yes no yes no no 415 Professor Xu Junfeng xujunf@gmail.com Wuyi University, Jiangmen, Guangdong, P. R. China
no no no no no 416 Professor Chen Wenjuan chenwenjuan@mail.sdu.edu.cn Shandong University, Jinan, Shandong, P. R. China
no no no no no 418 Professor Wang JinRong wjr9668@126.com Guizhou University, Guiyang, Guizhou, P. R. China
Nonlinear evolution equations; Impulsive differential equations; Fractional differential equations; Optimal controls; Fractional Hermite-Hadamard Inequalities.
 no no no no no 419 Professor Xiang X. Guizhou University, Guiyang, Guizhou, P. R. China
no no no no no 420 Professor Wei W. wwei@gzu.edu.cn Guizhou University, Guiyang, Guizhou, P. R. China
no no no no no 421 Professor Yarou M. Mustapha mfyarou@yahoo.com University of Jijel, Jijel, Algeria
no no no no no 422 Professor Prasad K. R. rajendra92@rediffmail.com Andhra University, Visakhapatnam, India
no no no no no 423 Professor Allaka Kameswararao kamesh_1724@yahoo.com GVP College of Engineering for Women, Madhurawada, INDIA, 530048
no no no no no 424 Professor Igbida J. jigbida@yahoo.fr UFR Mathématiques Appliquées et Industrielles, El Jadida, Maroc
no no no no no 425 Professor Wang Yuqing larawyq@126.com College of Science, Minzu University of China, Beijing, P. R. China
no no no no no 426 Professor He Xiaoming xmhe923@126.com College of Science, Minzu University of China, Beijing, P. R. China
no no no no no 427 Professor Wei Yuming ymwei@gxnu.edu.cn Beijing Institute of Technology, Beijing, P. R. China
no no no no no 428 Professor Wong Patricia J. Y. ejywong@ntu.edu.sg Nanyang Technological University, Singapore
no no no no no 429 Professor Chrif M. moussachrif@yahoo.fr Department of Mathematics, Faculty of Sciences of Fez, Fez, Morocco
no no no no no 430 Professor El Manouni S. manouni@hotmail.com Al-Imam University, Faculty of Sciences, Riyadh, KSA
no no no no no 431 Professor Kwiatkowski J. D. jdkwiatk@cord.edu Concordia College, Moorhead, MN, U.S.A.
no no no no no 433 Dr. Yang Aijun yangaij2004@163.com Zhejiang University of Technology, Hangzhou, Zhejiang, P. R. China
The boundary value problems of differential equations and nonlinear analysis.
 no no no no no 434 Professor Cheng Yuanji yuanji.cheng@mah.se Malmö University, Malmö, Sweden
no no no no no 435 Professor Badgire S. V. Kasubai, Gurukul Colony, Maharashtra, India
no no no no no 436 Professor El Farissi A. el.farissi.abdallah@caramail.com University of Mostaganem, Mostaganem, Algeria http://www.univ-mosta.dz/
no no no no no 438 Professor Aleroev T. S. Sultanovich aleroev@mail.ru Moscow Institute of Municipal Services and Construction, Moscow, Russia
no no no no no 439 Professor Aleroeva H. T. binsabanur@gmail.com Moscow Technical University of Communications and Informatics, Moscow, Russia
no no no no no 440 Professor Arjunan M. M. arjunphd07@yahoo.co.in C. B. M. College, Coimbatore- 641 042, Tamil Nadu, India
no no no no no 441 Professor Kavitha V. kavi_velubagyam@yahoo.co.in Karunya University, Karunya Nagar, Tamil Nadu, India
no no no no no 442 Doctor Akrout K. akroutkamel@gmail.com Larbi Tebissi University, Tebessa, Algeria
Partial Differential equations
 no no no no no 444 Professor Hernandez E. lalohm@icmc.usp.br Universidade de Sao Paulo, Sao Carlos SP, Brazil
no no no no no 445 Professor Henriquez H. R. hernan.henriquez@usach.cl Universidad de Santiago de Chile, Santiago, Chile
no no no no no 446 Professor Santos J. P. C. dos zepaulo@unifal-mg.edu.br Universidade Federal de Alfenas, Alfenas, MG, Brazil
no no no no no 447 Professor Shi Ailing Beijing University of Civil Engineering and Architecture, Beijing, P. R. China
no no no no no 449 Professor Xi Shouliang xishouliang@163.com University of Shanghai for Science and Technology, Shanghai, P. R. China
no no no no no 450 Professor Jia Mei jiamei-usst@163.com University of Shanghai for Science and Technology, Shanghai, P. R. China
no no no no no 451 Professor Ji Huipeng University of Shanghai for Science and Technology, Shanghai, P. R. China
no no no no no 452 Professor Murali P. murai_uoh@yahoo.co.in Andhra University, Visakhapatnam, India
no no no no no 453 Professor Suryanarayana N. V. V. S. VITAM College of Engineering, Visakhapatnam, India
no no no no no 454 Professor Gulgowski J. dzak@math.univ.gda.pl University of Gdansk, Gdansk, Poland
no no no no no 455 Dr. Karpuz B. bkarpuz@gmail.com Afyon Kocatepe University, Afyonkarahisar, Turkey http://www2.aku.edu.tr/~bkarpuz
Oscillation; Nonoscillation; Stability; Differential Equations; Difference Equations; Dynamic Equations; Time Scales
 no no no no no 456 dr. Šremr J. sremr@ipm.cz Institute of Mathematics, Academy of Sciences of the Czech Republic, Brno, Czech Republic
no no no no no 457 Professor Zada A. zadababo@yahoo.com Department of Mathematics, Abdul Wali Khan University Mardan, Pakistan
no no no no no 458 Professor Yu Shengqi yushengqi@126.com Nantong University, Nantong, P. R. China
Partial differential equations
 no no no no no 460 Professor Wang Youyu wang_youyu@163.com Tianjin University of Finance and Economics, Tianjin, P. R. China
no no no no no 462 Professor Yang Dandan ydd423@sohu.com School of Mathematical Science, Yangzhou University, Yangzhou, P. R. China
no no no no no 463 Professor Li Gang gli@yzu.edu.cn School of Mathematical Science, Yangzhou University, Yangzhou, P. R. China
no no no no no 464 Professor Pang Huihui phh2000@163.com College of Science, China Agricultural University, Beijing, P. R. China
no no no no no 465 Professor Ma Ya Shandong Normal University, Jinan, P. R. China
no no no no no 466 Professor Yan Baoqiang yanbqcn@yahoo.com.cn Shandong Normal University, Jinan, P. R. China
no no no no no 467 Professor Benmehidi S. samiabenmehidi@yahoo.fr Badji Mokhtar University, Annaba, Algeria
no no no no no 468 Professor Pinto M. pintoj@uchile.cl Universidad de Chile, Santiago, Chile
no no no no no 469 Professor Dong Qixiang qxdongyz@yahoo.com.cn School of Mathematical Science, Yangzhou University, Yangzhou, P. R. China
no no no no no 470 Professor Chen Ang ang.chen.jr@gmail.com Shandong University, Jinan, P. R. China
no no no no no 471 Professor Zhang Guowei zhirobo@yahoo.com.cn Shandong University, Jinan, P. R. China
no no no no no 472 Professor Adivar Murat murat.adivar@ieu.edu.tr Izmir University of Economics, Balcova, Izmir, Turkey http://homes.ieu.edu.tr/\symbol{126}madivar
Integral Equations, Difference Equations, Stability theory, Fixed point theory, Qualitative properties of differential, difference, and integral equations, dynamic equations on time scales.
 no no no no no 473 Professor Ali J. jahameed@fgcu.edu Florida Gulf Coast University, U.S.A.
no no no no no 474 Professor Perry D. dwp234@nyu.edu New York University, U.S.A
no no no no no 475 Prof. Sasi S. ss885@msstate.edu Mississippi State University, MS, U.S.A.
no no no no no 476 Professor Schaefer J. jrs244@dana.ucc.nau.edu Northern Arizona University, U.S.A.
no no no no no 477 Professor Schilling B. bls153@msstate.edu Mississippi State University, MS, U.S.A.
no no no no no 478 Professor Shivaji R. shivaji@ra.msstate.edu Mississippi State University, MS, U.S.A.
no no no no no 479 Professor Williams M. williamr@clarkson.edu Clarkson State University, U.S.A.
no no no no no 480 Professor Atici F. M. ferhan.atici@wku.edu Western Kentucky University, Bowling Green Kentucky, U.S.A,
Theory of Differntial Equations, Theory of Difference Equation, Calculus on Time Scales, Theory of Fractional Difference Equations
 no no no no no 481 Professor Avery R. I. rich.avery@dsu.edu Dakota State University, Madison, SD, U.S.A.
no no no no no 482 Professor Ballard G. M. grey.ballard@gmail.com Wake Forest University, Winston-Salem, NC, U.S.A.
no no no no no 483 Professor Baxley J. V. baxley@wfu.edu Wake Forest University, Winston-Salem, NC, U.S.A.
no no no no no 484 Professor Belinskiy B. P. Boris-Belinskiy@utc.edu The University of Tennessee at Chattanooga, Chattanooga, TN, U.S.A.
no no no no no 485 Professor Matthews J. V. Matt-Matthews@utc.edu The University of Tennessee at Chattanooga, Chattanooga, TN, U.S.A.
no no no no no 487 Professor Seba D. djam_seba@yahoo.fr Université de Boumerdes, Boumerdes, Algérie
no no no no no 488 Professor Du Zengji duzengji@163.com Xuzhou Normal University, Xuzhou, Jiangsu, P. R. China
no no no no no 489 Professor Kong Lingju Lingju-Kong @utc.edu University of Tennessee at Chattanooga, Chattanooga, TN, U.S.A. http://www.utc.edu/Academic/Mathematics/faculty/people.php
no no no no no 490 Professor Ehme J. jehme@spelman.edu Spelman College, Atlanta, GA, U.S.A.
no no no no no 491 Professor Guo Chengjun Guangdong University, of Technology, Guangzhou, Guangdong, P. R. China
no no no no no 492 Professor Xu Yuantong Sun Yat-sen University, Guangzhou, Guangdong, P. R. China
no no no no no 494 Professor O'Regan D. donal.oregan@nuigalway.ie National University of Ireland, Galway, Ireland
no no no no no 495 Professor Infante Gennaro gennaro.infante@unical.it Universita della Calabria, Cosenza, Italy www.mat.unical.it/~infante
Nonlocal boundary value problems for ODEs.
 no no no no no 496 Professor Pietramala P. pietramala@unical.it Universita della Calabria, Cosenza, Italy
no no no no no 497 Professor Kong Qingkai kong@math.niu.edu Northern Illinois University, DeKalb, IL, U.S.A.
no no no no no 499 Professor Kunkel C. ckunkel@utm.edu University of Tennessee, at Martin, Martin, TN, U.S.A.
no no no no no 500 Professor McArthur S. slmcarthur@ualr.edu University of Arkansas at Little Rock, Little Rock, AR, U.S.A.
no no no no no 501 Professor Rudd M. mrudd@uidaho.edu University of Idaho, Moscow, ID, U.S.A.
no no no no no 502 Professor Tisdell C. C. cct@unnsw.edu.au The University of New South Wales, Sidney, Australia
no no no no no 503 Professor Karunakaran R. Periyar University, Salem, Tamil Nadu, India
no no no no no 504 Professor Arockiasamy I. M. St. Paul's Hr. Sec. School, Salem, Tamil Nadu, India
no no no no no 505 Professor Wang Liancheng lwang5@kennesaw.edu Kennesaw State University, Kennesaw, GA, U.S.A.
no no no no no 506 Professor Wu Xiaoqin P. xpaul_wu@yahoo.com Mississippi Valley State University, Itta Bena, MS, U.S.A.
no no no no no 507 Professor Wang Haiyan haiyan.wang@asu.edu Arizona State University, Phoenix, AZ, U.S.A. PO Box 37100
no no no no no 509 Professor Lu Haihua lhh_xznu@yahoo.com.cn Nantong University, Nantong, P. R. China
no no no no no 510 Professor Aki Sueli M. Tanaka smtanaka@icmc.usp.br Universidade de Sao Paulo, Sao Carlos SP, Brazil
no no no no no 511 Professor Szymanska-Debowska Katarzyna Malgorzata grampa@zbiorcza.net.lodz.pl Technical University of Lodz, Lodz, Poland
no no no no no 512 Professor Ehrke J. john.ehrke@acu.edu Abilene Christian University, Abilene, TX, U.S.A. http://math.acu.edu/ehrke/
no no no no no 513 Professor Saifi O. saifi_kouba@yahoo.fr Algiers University, Algiers, Algeria
no no no no no 514 Professor Marcos A. abmarcos@imsp-uac.org Institut de Mathématiques et de Sciences Physiques, Porto Novo, Benin
no no no no no 515 Professor Shibata T. shibata@amath.hiroshima-u.ac.jp Hiroshima University, Higashi-Hiroshima, Japan
no no no no no 516 Professor Mukhigulashvili S. mukhig@ipm.cz Academy of Sciences of the Czech Republic, Brno, Czech Republic
no no no no no 517 Professor Grytsay I. grytsay@mail.univ.kiev.ua Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
no no no no no 518 Doctor Li Tongxing litongx2007@163.com Shandong University, Jinan, Shandong, P. R. China
oscillation theory of differential equations, difference equations, and dynamic equations on time scales
no no no no no 519 Professor Han Zhenlai hanzhenlai@163.com University of Jinan, Jinan, Shandong, P. R. China
no no no no no 520 Professor Sun Shurong sshrong@163.com University of Jinan, Jinan, Shandong, P. R. China
no no no no no 521 Professor Zhang Chenghui zchui@sdu.edu.cn Shandong University, Jinan, Shandong, P. R. China
no no no no no 522 Professor Tiryaki A. aydin.tiryaki@izmir.edu.tr Izmir University, Uckuyular, Izmir, Turkey http://www.izmir.edu.tr/tr/images/stories/Aydin_Tiryaki_CV_English_2011.pdf
Differential Equations: Oscillation, Stability, Boundedness, Periodicity.
Functional Differential Equations: Oscillation, Positive solutions.
Lyapunov's type Inequalities.
Difference Equations.
 no no no no no 523 Professor Murty M. S. N. drmsn2002@gmail.com Department of Mathematics, Acharya Nagarjuna University - NagarjunaNagar Guntur- 522510, India.
no no no no no 524 Professor Kumar G. Suresh drgsk006@gmail.com Koneru Lakshmaiah University, Vaddeswaram, India
no no no no no 525 Professor Xu Hong-Yan xhyhhh@126.com Jingdezhen Ceramic Institute, Jingdezhen, Jiangxi, P. R. China
Complex analysis, Nevanlinna theory, Complex differential equation
 no no no no no 526 Professor Cao Ting-Bin tbcao@ncu.edu.cn Nanchang University, Nanchang, Jiangxi, P. R. China Department of Mathematics
Complex analysis, Complex differential equations, Complex difference equations
 no no no no no 527 Professor Vijaya M. vijayaanbalacan@gmail.com Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India
no no no no no 528 Professor Tu Jin tujin2008@sina.com Jiangxi Normal University, Nanchang, P. R. China
complex linear differential equation; complex difference equation; value distribution theory,
 no no no no no 529 Professor Long Teng Jiangxi Normal University, Nanchang, P. R. China
no no no no no 530 Dr Annamalai Anguraj angurajpsg@yahoo.com PSG College of Arts and Science, Coimbatore, Tamil Nadu, India
Impulsive Differential System, Partial Differential Equations,Differential Inclusions, Computational PDE
 no no no no no 531 Assistant Professor Vinodkumar A. vinod026@gmail.com PSG College of Technology, Coimbatore, Tamil Nadu, India.
Stochastic/deterministic Differential Equations/ Inclusions.
 no no no no no 532 Professor Wu Baofeng University of Shanghai for Science and Technology, Shanghai, P. R. China
no no no no no 533 Associate Professor Vrabel Robert robert.vrabel@stuba.sk Slovak Technical University Bratislava, Institute of Applied Informatics, Automation and Mathematics, Trnava, Slovakia
no no no no no 534 Professor Yao Kouadio D. kdyao@ualr.edu University of Arkansas at Little Rock, Little Rock, AR, U.S.A.
no no no no no 535 Professor Pachpatte Deepak B pachpatte@gmail.com Dr. B. A. M. University, Aurangabad, Maharashtra, India
Differential Equations, Integral Equations, Dynamical Equations On Time scales
 no no no no no 536 Professor Daddiouaissa Elhachemi dmhbsdj@gmail.com University Kasdi Merbah, Ouargla, Algeria
no no no no no 537 Professor Tunc C. cemtunc@yahoo.com Yüzüncü Yil University, Van, Turkey
Stability, instability, boundedness, asymptotic behaviors, oscillation, non-oscillation of solutions, Lyapunov functions and functional for Ordinary Differential Equations and Functional Differential Equations.
 no no no no no 538 Professor Balachandran K. kbkb1956@yahoo.com Bharathiar University, Coimbatore, India
no no no no no 540 Professor Kiruthika S. Bharathiar University, Coimbatore, India
no no no no no 541 Professor Peng Lequn penglq1956@yahoo.com.cn Hunan University of Arts and Science, Changde, Hunan, P. R. China
no no no no no 542 Professor Wang Wentao wentaowang2009@yahoo.com.cn College of Mathematics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang, P. R. China
no no no no no 543 Professor Fan Qiyi Hunan University of Arts and Science, Changde, Hunan, P. R. China
no no no no no 544 Professor Yi Xuejun yixuejunhd@yahoo.cn College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, P. R. China
no no no no no 545 Professor Huang Lihong College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, P. R. China
no no no no no 546 Professor Lupulescu V. lupulescu_v@yahoo.com Constantin Brancusi University, Targu-Jiu, Romania
no no no no no 547 Professor Benseridi Hamid m_benseridi@yahoo.fr Department of Mathematics, Faculty of Science, Sétif University, 19000, Algeria
Applied Mathematics, PDEs
 no no no no no 548 Professor Dilmi M. mouraddil@yahoo.fr University Med Boudiaf, M'sila, Algeria
no no no no no 549 Professor Sun Jian-Ping jpsun@lut.cn Lanzhou University of Technology, Lanzhou, Gansu, P. R. China
no no no no no 550 Professor Ren Qiu-Yan Lanzhou University of Technology, Lanzhou, Gansu, P. R. China
no no no no no 551 Dr. Liu Wenjun wjliu@nuist.edu.cn Nanjing University of Information Science and Technology, Nanjing, P. R. China
no no no no no 552 Professor Mao Jinxiu maojinxiu1982@163.com Qufu Normal University, Qufu, Shandong, P. R. China
no no no no no 553 Professor Zhao Zengqin zqzhao@mail.qfnu.edu.cn Qufu Normal University, Qufu, Shandong, P. R. China
no no no no no 554 Professor Xu Naiwei dahai009@126.com Shandong Water Conservation Professional Institute, Rizhao, Shandong, P. R. China.
no no no no no 556 Professor Xu Fuyi zbxufuyi@163.com Shandong University of Technology, Zibo, Shandong, P. R. China
no no no no no 557 Professor Bounkhel Messaoud bounkhel@ksu.edu.sa King Saud University, Riyadh, Saudi Arabia
Optimization, Nonsmooth Analysis, Variational Inequalities, Differential Inclusions
 no no no no no 558 Professor Al-Senan B. King Saud University, Riyadh, Saudi Arabia
no no no no no 559 Professor Akhiev S. S. axiyev@rambler.ru Azerbaijan State Pedagogical University, Baku, Azerbaijan
no no no no no 560 Professor Long Wei hopelw@126.com Jiangxi Normal University, Nanchang, Jiangxi, P. R. China
no no no no no 561 Professor Zhang Hong-Xia Jiangxi Normal University, Nanchang, Jiangxi, P. R. China
no no no no no 562 Professor Remili M. m.remili@yahoo.fr University of Oran, Oran, Algeria
no no no no no 563 Professor Zhao Ya-Hong Lanzhou University of Technology, Lanzhou, Gansu, P. R. China
no no no no no 564 Professor Ke Yuanyuan ke_yy@163.com Renmin University of China, Beijing, P. R. China
no no no no no 566 Professor Ding Jian df2001101@126.com College of Math and statistics, Nanjing University of Information Science and Technology,Nanjing 210044, China
no no no no no 567 Professor Xu Junxiang xujun@seu.edu.cn Southeast University, Nanjing, P. R. China
no no no no no 568 Professor Zhang Fubao zhangfubao@seu.edu.cn Southeast University, Nanjing, P. R. China
no no no no no 569 Professor Hamani K. hamanikarima@yahoo.fr University of Mostaganem, Mostaganem, Algeria http://www.univ-mosta.dz/
no no no no no 570 Professor Shibuya Akihito Akihito.Shibuya@gmail.com Kumamoto University, Kurokami, Kumamoto, Japan
no no no no no 571 Professor Tanigawa T. tanigawa@educ.kumamoto-u.ac.jp Kumamoto University, Kurokami, Kumamoto, Japan
no no no no no 572 Dr. Özbekler Abdullah abdullah@atilim.edu.tr Atilim University, Ankara, Turkey http://www.atilim.edu.tr/~ozbekler/
Ordinary and Partial Differential Equations, Impulsive Differential Equations,
Functional Differential Equations, Difference Equations, Time Scale Calculus.

 no no no no no 573 Professor Zafer A. zafer@metu.edu.tr Middle East Technical University, Ankara, Turkey
differential equations, difference equation, time scale calculus
 no no no no no 574 Professor Yuan Chengjun ycj7102@163.com Harbin University, Harbin, Heilongjiang, P. R. China
no no no no no 575 Professor Bai Zhanbing zhanbingbai@163.com Shandong University of Science and Technology, Qingdao, P. R. China
no no no no no 576 Professor Lv Zhi-Wei sdlllzw@mail.ustc.edu.cn University of Science and Technology of China, Hefei, Anhui, P. R. China
no no no no no 577 Professor Liang Jin jinliang@sjtu.edu.cn Shanghai Jiao Tong University, Shanghai, P. R. China
no no no no no 579 Professor Tang Yantao Tianjin University of Finance and Economics, Tianjin, P. R. China
no no no no no 580 Professor Zhao Meng Tianjin University of Finance and Economics, Tianjin, P. R. China
no no no no no 581 Professor Guan Yujing Jilin University, Changchun, P. R. China http://www.jlu.edu.cn/
no no no no no 584 Professor Baculikova B. blanka.baculikova@tuke.sk Technical University of Kosice, Kosice, Slovakia
no no no no no 585 Professor Dzurina J. jozef.dzurina@tuke.sk Technical University of Kosice, Kosice, Slovakia
oscillation theory of functional differential equations with deviating argument
 no no no no no 586 Professor Zhang Xingqiu zhxq197508@163.com Liaocheng University, Liaocheng, Shandong, P. R. China
no no no no no 587 Professor Sun Jingxian jxsun7083@sohu.com Xuzhou Normal University, Xuzhou, Jiangsu, P. R. China
no no no no no 589 Professor Mu Chunlai chunlaimu@yahoo.com.cn Chongqing University, Chongqing, P. R. China
no no no no no 590 Professor Chiu Kuo-Shou kschiu@umce.cl Universidad Metropolitana de Ciencias de la Educacion, Santiago, Chile
no no no no no 591 Professor Chang Yong-Kui lzchangyk@163.com Lanzhou Jiaotong University, Lanzhou, P. R. China
no no no no no 592 Professor Zhao Zhi-Han zhaozhihan841110@126.com Lanzhou Jiaotong University, Lanzhou, P. R. China
no no no no no 593 Professor Nieto Juan J. juanjose.nieto.roig@usc.es Universidad de Santiago de Compostela, Santiago de Compostela, Spain
Nonlinear analysis
Fractional differential equations
Impulsive differential equations
Biomedical applications
 no no no no no 594 Professor Oinarov Ryskul. o_ryskul@mail.ru L. N. Gumilev Eurasian National University, Kazakhstan http://www.enu.kz/en/professors/prepodavateli/oinaruly/index.php
RESEARCH INTERESTS:

Major research interests are in the theory of functions, functional analysis and the theory of differential equations:

- Linear and nonlinear integral and matrix operators;

- Weighted inequalities;

- Weighted embedding theorem;

- Spectral theory of operators;

- The qualitative properties of quasilinear differential and difference equations.
no no no no no 595 Professor Rakhimova S. Y. rakhimova.salta@mail.ru L. N. Gumilev Eurasian National University, Kazakhstan
no no no no no 596 Professor Zhou Yong yzhou@xtu.edu.cn Xiangtan University, Xiangtan, Hunan, P. R. China
no no no no no 597 Professor He Yun-Yun Xiangtan University, Xiangtan, Hunan, P. R. China
no no no no no 598 Professor Tian Yuansheng tys73@163.com Department of Mathematics, Xiangnan University, Chenzhou, Hunan, P. R. China
no no no no no 599 Professor Liu Dengming liudengming08@163.com Chongqing University, Chongqing, P. R. China
no no no no no 600 Professor Yang Ying yiyiying729@163.com Shenzhen University, Shenzhen, P. R. China
no no no no no 601 Professor Jin Chunhua jinchhua@126.com South China Normal University, Guangzhou, P. R. China
no no no no no 603 Professor Mostefai F. fatymath@gmail.com Université de Saida, Saida, Algérie
no no no no no 605 Doctor Li Haitao haitaoli09@gmail.com Shandong University, Jinan, P. R. China
Boundary value problem,Switched system,Biological system,Logical system
 no no no no no 606 Professor Liu Yansheng yanshliu@gmail.com Shandong Normal University, Jinan, P. R. China
no no no no no 607 Professor Xu Huiye silviahsu2005@yahoo.com.cn North University of China, Taiyuan, Shanxi, P. R. China
no no no no no 608 Professor Li Fang fangli860@gmail.com Yunnan Normal University, Kunming, P. R. China
no no no no no 609 Professor Liu James H. liujh@jmu.edu James Madison University, Harrisonburg, VA, U.S.A.
no no no no no 610 Professor Mophou G. M. gmophou@univ-ag.fr Universite des Antilles et de La Guyane, Campus Fouillole, Guadeloupe
no no no no no 611 Professor Milisic J. P. pina.milisic@fer.hr University of Zagreb, Zagreb, Croatia
no no no no no 612 Professor Zupanovic V. University of Zagreb, Zagreb, Croatia
no no no no no 613 Professor Piramanantham V. piramanantham@yahoo.co.in Bharathidasan University, Tiruchirappalli, India
no no no no no 614 Professor Wei Junjie weijj@hit.edu.cn Harbin Institute of Technology, Harbin, P. R. China
Bifurcation Theory of Differential Equations with Delays.
 no no no no no 615 Professor Wei Yuan Beijing Institute of Strength and Environment, Beijing, P. R. China
no no no no no 616 Professor Xu Meihong Harbin Institute of Technology Harbin, P. R. China
no no no no no 617 Professor Xie Feng fxie@dhu.edu.cn Donghua University Shanghai, P. R. China
Singular perturbations in ODES
 no no no no no 618 Professor Jin Zhaoyang Donghua University Shanghai, P. R. China
no no no no no 619 Professor Ni Mingkang xiaovikdo@163.com East China Normal University, Shanghai, P. R. China
no no no no no 620 Professor Mashiyev R. A. mrabil@dicle.edu.tr Dicle University, Diyarbakir, Turkey http://www.dicle.edu.tr/akademikweb/index.php?orta=goster2&gsn=9999&birim=3&bolum=1&altbolum=0
Variational method, Sobolev and Lebesgue spaces with variable exponent, Elliptic and Parabolic equations, p-Laplacian, p(x)-Laplacian, discrete boundary value problem, Hardy type inequalities, Sobolev type inequalities
 no no no no no 621 Professor Cekic B. bilalc@dicle.edu.tr Dicle University, Diyarbakir, Turkey
no no no no no 622 Professor Buhrii O. M. ol_buhrii@i.ua Ivan Franko National University of Lviv, Lviv, Ukraine
no no no no no 623 Professor Wang Guangwa wgw7653@xznu.edu.cn Xuzhou Normal University, Xuzhou, P. R. China
no no no no no 624 Professor Sun Li slwgw-7653@xznu.edu.cn China University of Mining and Technology, Xuzhou, P. R. China
no no no no no 625 Professor Zhou Mingru zhoumr@xznu.edu.cn Xuzhou Normal University, Xuzhou, P. R. China
no no no no no 626 Professor Alzabut J. O. jalzabut@psu.edu.sa Prince Sultan University, Riyadh, Saudi Arabia
no no no no no 627 Professor Mukheimer A. Prince Sultan University, Riyadh, Saudi Arabia
no no no no no 629 Professor Li Lei-Min leiminli@hotmail.com Nanchang University, Nanchang, Jiangxi, P. R. China
no no no no no 630 Professor Liu Zhenhai zhhliu@hotmail.com Guangxi University for Nationalities, Nanning, Guangxi, P. R. China
no no no no no 631 Professor Szántó I. ivan.szanto@usm.cl Universidad Tecnica Federico Santa Maria, Valparaiso, Chile
no no no no no 632 Professor Sáez E. eduardo.saez@usm.cl Universidad Tecnica Federico Santa Maria, Valparaiso, Chile
no no no no no 633 Prof. Ferreira Rui ruiacferreira@ulusofona.pt Lusophone University of Humanities and Technologies, Lisbon, Portugal http://paginas.ulusofona.pt/p3364
Fractional Calculus
 no no no no no 634 Professor Chen Peng pengchen729@sina.com China Three Gorges University, Yichang, Hubei, P. R. China
differential equations and inclusions, critical point theory
 no no no no no 635 Professor Xiao Li xiaolimaths@sina.com Central South University, Changsha, Hunan, P. R. China
no no no no no 636 Professor Saadi A. Abdsaadi@yahoo.fr Bechar University, Bechar, Algeria
no no no no no 637 Professor Benbachir M. mbenbachir2001@yahoo.fr Bechar University, Bechar, Algeria
no no no no no 639 Professor Boscaggin A. boscaggi@sissa.it SISSA, International School for Advanced Studies Via Bonomea, Trieste, Italy
no no no no no 640 Professor Garrione M. garrione@sissa.it SISSA, International School for Advanced Studies Via Bonomea, Trieste, Italy
no no no no no 642 Professor Song Ruipeng Shanxi University, Taiyuan, Shanxi, P. R. China
no no no no no 643 Professor Xiao Yu University of Shanghai for Science and Technology, Shanghai, P. R. China
no no no no no 644 Professor Chen Jianming University of Shanghai for Science and Technology, Shanghai, P. R. China
no no no no no 646 Professor Wang Xiaojing wangxj2010106@sohu.com Huaiyin Normal University, Huaian, Jiangsu, P. R. China
no no no no no 652 Professor Ardjouni A. abd_ardjouni@yahoo.fr University of Annaba, Annaba, Algeria
no no no no no 653 Professor Djoudi A. adjoudi@yahoo.com University of Annaba, Annaba, Algeria
no no no no no 654 Professor Affane D. affanedoria@yahoo.fr Université de Jijel, Jijel, Algérie
no no no no no 657 Professor Belakroum D. belakroum05@yahoo.fr University Badji Mokhtar, Annaba, Algeria
no no no no no 658 Professor Guezane-Lakoud A. a_guezane@yahoo.fr University Badji Mokhtar, Annaba, Algeria
no no no no no 662 Professor Ge Bin gebin04523080261@163.com Harbin Engineering University, Harbin, P. R. China
Nonlinear Function Analysis, Partial Differential Equations (Elliptic Differential inclusion problem); variable exponent inclusion problem
 no no no no no 663 Professor Zhou Qingmei zhouqingmei2008@163.com Northeast Forestry University, Harbin, P. R. China
no no no no no 665 Professor Arshad S. sadia_735@yahoo.com Government College University, Abdus Salam School of Mathematical Sciences (ASSMS), Lahore, Pakistan
no no no no no 666 Professor Nosheen A. hafiza_amara@yahoo.com Government College University, Abdus Salam School of Mathematical Sciences (ASSMS), Lahore, Pakistan
no no no no no 667 Professor Calder M. S. m2calder@math.uwaterloo.ca University of Waterloo, Waterloo, Ontario, Canada
no no no no no 668 Professor Siegel D. dsiegel@math.uwaterloo.ca University of Waterloo, Waterloo, Ontario, Canada
no no no no no 669 dr Cecchini S. cecchini@math.unifi.it University of Modena and Reggio Emilia, Italy
no no no no no 670 Professor Malaguti L. luisa.malaguti@unimore.it University of Modena and Reggio Emilia, Italy
boundary value problems, reaction-diffusion equations, multivalued analysis and evolution equations
 no no no no no 671 Professor Taddei V. valentina.taddei@unimore.it University of Modena and Reggio Emilia, Italy
no no no no no 672 Lecture Ji Chao jichao@ecust.edu.cn East China University of Science and Technology, Shanghai, P. R. China
nonlinear functional analysis, critical point theory
 no no no no no 676 DR Derhab Mohammed derhab@yahoo.fr University Abou-Bekr Belkaid Tlemcen, Tlemcen, Algeria
Boundary Value Problems.
 no no no no no 677 Professor Zahar S. zahar_samira@yahoo.fr University Abd-Errahmane Mira, Bejaia, Algeria
no no no no no 680 Professor Usman M. Muhammad.Usman@notes.udayton.edu University of Dayton, Dayton, Ohio, U.S.A.
no no no no no 681 Professor Fuentes C. G. cristina.fuentes.gomez@gmail.com Universidad de Santiago de Chile, Santiago, Chile
no no no no no 686 Professor Yang Zhilin zhilinyang@sina.com Qingdao Technological University, Qingdao, Shandong, P. R. China
no no no no no 688 Professor Zhang Lihong zhanglih149@126.com Shanxi Normal University, Linfen, Shanxi, P. R. China
no no no no no 689 Professor Wang Guotao wgt2512@163.com Shanxi Normal University, Linfen, Shanxi, P. R. China
no no no no no 690 Professor Galewski Marek marek.galewski@p.lodz.pl Technical University of Lodz, Lodz, Poland
no no no no no 695 Professor Zhang Jian chjmath@yahoo.com.cn Shandong University, Jinan, Shandong, P. R. China
no no no no no 697 Professor Cao Jianxin cao.jianxin@hotmail.com Central South University, Changsha, Hunan, P. R. China
no no no no no 700 Professor Ding Hui-Sheng dinghs@mail.ustc.edu.cn Jiangxi Normal University, Nanchang, Jiangxi, P. R. China
no no no no no 701 Professor Fu Jiu-Dong 563989457@qq.com Jiangxi Normal University, Nanchang, Jiangxi, P. R. China
no no no no no 704 Professor Hazi M. hazi@ens-kouba.dz Ecole Normale Superieure, Kouba, Algiers, Algeria
no no no no no 705 Professor Bragdi M. bragdimabrouk@gmail.com Larbi Ben M'Hidi University, OEB, Algeria.
Optimal control, abstract differential equations with fractional orders
 no no no no no 716 Dr. Ibrahim Rabha W. rabhaibrahim@yahoo.com Institute of Mathematical Sciences, University Malaya, Kuala Lumpur, Malaysia
no no no no no 717 Dr. Sun Jiebao sunjiebao@126.com Harbin Institute of Technology, Harbin, P. R. China
no no no no no 718 Professor Zhang Dazhi Harbin Institute of Technology, Harbin, P. R. China
no no no no no 719 Professor Wu Boying mathwby@hit.edu.cn Harbin Institute of Technology, Harbin, P. R. China
no no no no no 722 Professor Zhang Cui-Yan zhcy0618@163.com Jiangxi Normal University, Nanchang, P. R. China
no no no no no 726 Professor Kalas J. kalas@math.muni.cz Masaryk University, Brno, Czech Republic
Ordinary differential equations, stability theory, asymptotic behaviour of solutions
 no no no no no 727 Professor Rebenda J. rebenda@math.muni.cz Masaryk University, Brno, Czech Republic
no no no no no 733 Professor Yao Zheng'an mcsyao@mail.szu.edu.cn Sun Yat-sen University, Guangzhou, P. R. China
no no no no no 741 Professor Megan M. megan@math.uvt.ro Academy of Romanian Scientists, Bucharest, Romania
no no no no no 742 Professor Ceausu Traian ceausu@math.uvt.ro West University of Timisoara, Timisoara, Romania
no no no no no 743 dr Minda A. A. a.minda@uem.ro Eftimie Murgu University of Resita, Resita, Romania
no no no no no 756 Professor Vítovec J. vitovec@feec.vutbr.cz Brno University of Technology, Brno, Czech Republic
no no no no no 770 Professor Liu Lishan lls@mail.qfnu.edu.cn School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, P. R. China
no no no no no 775 Prof. Vas G. vasg@math.u-szeged.hu Analysis and Stochastic Research Group of the Hungarian Academy of Sciences, University of Szeged, Hungary
no no no no no 777 Professor Huang Wentao huangwentao@163.com Guilin University of Electronic Technology, Guilin, Guangxi, P. R. China http://w3.guet.edu.cn/dept7/people/TeacherDetail.Asp?TeacherID=275
Limit cycles, isochronous center, critical period bifurcation,traveling wave solution of nolinear wave equations.
 no no no no no 778 Professor Fan Xingyu fanxingyu666888@163.com Guilin University of Electronic Technology, Guilin, Guangxi, P. R. China
no no no no no 779 Professor Chen Xingwu xingwu.chen@hotmail.com Sichuan University, Chengdu, Sichuan, P. R. China
no no no no no 780 Professor Yang Xiang Dong yangsddp@126.com Kunming University of Science and Technology, Kunming, P. R. China
no no no no no 781 Professor Li Xingchang lxctsq@163.com Qufu Normal University Qufu, Shandong, P. R. China
no no no no no 804 Dr Fang Zheng fangzhengjd@126.com Jiangnan University, Wuxi, P. R. China
no no no no no 805 Professor Yang Yongqing yyq640613@gmail.com Jiangnan University, Wuxi, P. R. China
Qualitative Theory
 no no no no no 814 Professor Zhu Zhi-Qiang z3825@yahoo.com.cn Guangdong Polytechnic Normal University, Guangzhou, P. R. China
no no no no no 816 Professor Zhuang Kejun zhkj123@163.com Anhui University of Finance and Economics, Bengbu, P. R. China
no no no no no 817 Professor Wen Zhaohui wzh590624@sina.com Anhui University of Finance and Economics, Bengbu, P. R. China
no no no no no 818 Professor Zhou Huacheng hilbertstory@163.com Donghua University Shanghai, P. R. China
no no no no no 819 Professor Kou Chunhai kouchunhai@dhu.edu.cn Donghua University Shanghai, P. R. China
no no no no no 821 Professor Chen Fulai cflmath@163.com Xiangnan University, Chenzhou, P. R. China
fractional differential equations
 no no no no no 828 Professor Tatar N. tatarn@kfupm.edu.sa King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia http://www.univ-annaba.net/
no no no no no 835 Professor Dong Wei wdongau@yahoo.com.cn Hebei University of Engineering, Handan, Hebei, P. R. China
no no no no no 836 Professor Wei Zhongli jnwzl@yahoo.com.cn Shandong Jianzhu University, Jinan, Shandong, P. R. China
no no no no no 852 Professor Chen Xu woshchxu@163.com Liaocheng University, Liaocheng, Shandong, P. R. China
no no no no no 853 Professor Yang Chen yangchen0809@126.com Business College of Shanxi University, Taiyuan, P. R. China
no no no no no 854 Professor Yan Jurang Shanxi University, Taiyuan, Shanxi, P. R. China
no no no no no 855 Professor Chen Lizhen Yangzhou University, Yangzhou, Jiangsu, P. R. China
no no no no no 856 Professor Fan Zhenbin fzbmath@yahoo.com.cn Changshu Institute of Technology, Suzhou, Jiangsu, P. R. China
no no no no no 857 Professor Burton T. A. taburton@olypen.com Northwest Research Institute, Port Angeles, WA, U.S.A. http://www.math.siu.edu/burton/
yes yes no yes no 858 Professor Hatvani L. hatvani@math.u-szeged.hu Bolyai Institute, University of Szeged, Hungary http://www.math.u-szeged.hu/~hatvani
yes no yes yes no 860 Professor Lyons J. jeff.lyons@tamucc.edu Texas A&M University, Corpus Christi, TX, U.S.A.
no no no no no 863 Prof. Yucedag Z. zehra@dicle.edu.tr Dicle University, Diyarbakir, Turkey
no no no no no 864 Prof. Ogras S. sogras@dicle.edu.tr Dicle University, Diyarbakir, Turkey)
no no no no no 865 Professor Wang Helin whl982032@163.com Zhejiang University of Technology, Hangzhou, Zhejiang, P. R. China
no no no no no 866 Professor Villari G. villari@math.unifi.it 'Ulisse Dini' of Florence, Firenze, Italy http://web.math.unifi.it/users/villari/
ordinary differential equations, qualitative theory
 yes no no no no 867 Professor Murakami S. murakami@youhei.xmath.ous.ac.jp Okayama University of Science, Okayama, Japan http://www.ous.ac.jp/english/index.html
ordinary differential equations, functional differential equations
 yes no no no no 872 Prof Villaseñor Gabriel gabrielvillaseor@gmail.com Universidad Michoacana de san Nicolas de Hidalgo, Michoacán, Mexico
Dynamical systems
 no no no no no 873 Dr. Osuna Osvaldo osvaldo@ifm.umich.mx Instituto de Física y Matemáticas, Universidad Michoacana, Michoacán, Mexico http://www.ifm.umich.mx/Matematicas/Academicos/osuna.html
Qualitative th. of differential eqs., Dynamical systems (Lagrangian dynamic, ergodic theory), differential geometry.
 no no no no no 878 Prof. Baek H. hkbaek@cu.ac.kr Catholic University of Daegu, Kyeongsan, Kyeongbuk, South Korea
Nonlinear Dynamics, Biological Mathematics
 no no no no no 893 Prof. Sun Yibing sun_yibing@126.com University of Jinan, Jinan, Shandong, P. R. China
no no no no no 894 Prof. Sun Ying ss_suny@ujn.edu.cn University of Jinan, Jinan, Shandong, P. R. China
no no no no no 896 dr Wang Jian pdejwang@163.com Ocean University of China, Qingdao, Shandong, P. R. China
partial differential equation
 no no no no no 898 Prof. Ge Yanyan geyanyan19871987@163.com Ocean University of China, Qingdao, Shandong, P. R. China
no no no no no 899 Professor Bie Qunyi biequnyi@yahoo.com.cn College of Science, China Three Gorges University, Yichang City, Hubei Province, P. R. China
Partial Differential Equation
 no no no no no 900 Dr. Panigrahi S. spsm@uohyd.ernet.in University of Hyderabad, Hyderabad, India
Qualitative theory of differential equations, Functional differential equations,
Inequalities, Dynamic Equations on Time Scales.
 no no no no no 901 Professor Buse C. buse1960@gmail.com West University of Timisoara, Timisoara, Romania
Ordinary differential equations, Semigroups of operators, Control Theory
 no no no no no 904 Dr. Zhao Xiaopeng zxp032@gmail.com College of Mathematics, Jilin University, P. R. China
no no no no no 910 Professor Jia Gao gaojia89@163.com University of Shanghai for Science and Technology, Shanghai, P. R. China
partial differential equations, nonlinear analysis
no no no no no 915 Professor He Xiaofei hxfcsu@sina.com Jishou University, Jishou, Hunan, P. R. China
no no no no no 918 Dr. Danet C.-P. cristiandanet@yahoo.com University of Craiova, Craiova, Romania
Partial Differential Equations
 no no no no no 926 Dr Chung Nguyen Thanh ntchung82@yahoo.com Quang Binh University, Dong Hoi, Quang Binh, Vietnam
no no no no no 929 Professor Ize J. jil@mym.iimas.unam.mx National Autonomous University of Mexico, Mexico http://serpiente.dgsca.unam.mx/rectoria/htm/demo2.html
bifurcation theory, variational methods, topological methods
 yes no no no no 935 Professor Szijártó A. szijarto@math.u-szeged.hu Bolyai Institute, Szeged, Hungary
no no no no no 940 Prof. Pan Shuxia shxpan@yeah.net Lanzhou University of Technology, Lanzhou, Gansu, P. R. China
no no no no no 946 Dr. Xia Li xaleysherry@163.com Shenzhen University, Shenzhen, Guangdong, P. R. China
Theories on parabolic and elliptic equations
 no no no no no 947 Professor Diagana T. tokadiag@gmail.com Howard University, Washington, DC, U.S.A.
no no no no no 948 Prof. Székely L. szekely.laszlo@gek.szie.hu Szent István University, Institute of Mathematics and Informatics, Gödöllő
no no no no no 949 Prof. Li Jingna jingna8005@hotmail.com Jinan University, Guangzhou, P. R. China
no no no no no 951 Graduate Student Ko Eunkyung ek94@msstate.edu Mississippi State University, MS, U.S.A.
no no no no no 952 Professor Lee Eun Kyoung lek915@pusan.ac.kr Pusan National University, Busan, South Korea
no no no no no 957 dr Wu Limeng neamou123@163.com East China Normal University, Shanghai, P. R. China
Singular perturbation theory, Operational Research and Cybernetics
 no no no no no 960 Prof. Braverman E. maelena@math.ucalgary.ca University of Calgary, Calgary, Canada http://math.ucalgary.ca/~maelena/
delay differential equations, difference equations, equations of mathematical biology
yes no no no no 961 Professor Jimenez S. sjimenez@ubolivariana.cl Universidade Bolivariana, Los Angeles, Chile
no no no no no 967 Prof. Komornik V. vilmos.komornik@math.unistra.fr Université de Strasbourg, Strasbourg, France http://www-irma.u-strasbg.fr/~komornik/
control theory of partial differential equations
 yes no no no no 973 Professor Wang Yong ywangsc@gmail.com Southwest Petroleum University, Chengdu, Sichuan, P. R. China
no no no no no 974 Prof. Zhang Liehui zhangliehui@vip.163.com State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan, P. R. China
no no no no no 975 Professor Lu Haibo classten@163.com East China Normal University, Shanghai, P. R. China
no no no no no 994 Prof. Liska V. vladimir.liska@stuba.sk Institute of Applied Informatics, Automation and Mathematics, Trnava, Slovakia
no no no no no 995 Prof. Mankova I. ingrida.mankova@gmail.com Institute of Applied Informatics, Automation and Mathematics, Trnava, Slovakia
no no no no no 999 Prof. Younus A. awaissms@yahoo.com Government College University, Abdus Salam School of Mathematical Sciences, (ASSMS), Lahore, Pakistan
no no no no no 1008 Professor Djebali S. djebali@hotmail.com Department of Mathematics, Ecole Normale Superueure, Kouba, Algeria
Ordinary Differential Equations and Inclusions. Fixed point Theory.
 no no no no no 1010 dr Mohamed Mesliza mesliza@hotmail.com Universiti Teknologi MARA (Perlis), Arau, Perlis, Malaysia
ordinary differential equations
 no no no no no 1012 Prof. Fan Meng xmath111@hotmail.com Northeast Normal University, Changchun, P. R. China
no no no no no 1013 Prof. Xia Zhinan xiazn299@hotmail.com Northeast Normal University, Changchun, P. R. China
no no no no no 1019 Prof. Zhai Chengbo cbzhai@sxu.edu.cn Shanxi University, Taiyuan, P. R. China
Nonlinear functional Analysis and Differential Equations
 no no no no no 1035 Prof. Zhao Mei-ling zhaomeiling0@126.com University of Shanghai for Science and Technology, Shanghai, P. R. China
no no no no no 1055 Prof. Thompson Bevan hbt@maths.uq.edu.au The University of Queensland, Queensland, Australia
no no no no no 1056 Prof. Jusoh Muhammad Sufian mdsufian@perlis.uitm.edu.my Universiti Teknologi MARA (Perlis), Arau, Perlis, Malaysia
no no no no no 1059 Prof. Stavroulakis I. P. ipstav@cc.uoi.gr University of Ioannina, Ioannina, Greece
no no no no no 1061 Dr. Cakmak D. dcakmak@gazi.edu.tr Gazi University, Ankara, Turkey http://websitem.gazi.edu.tr/site/dcakmak
no no no no no 1062 Prof. Ma Junchi majunchi2009@163.com College of Science, Yanshan University, Qinhuangdao, Hebei, P. R. China
fractional differential equations
 no no no no no 1063 Prof. Yang Jun jyang@ysu.edu.cn College of Science, Yanshan University, Qinhuangdao, Hebei, P. R. China
no no no no no 1065 Prof. Yang Mingquan mingquanyang2008@yahoo.com.cn Jiaxing University, Jiaxing, P. R. China
Functional Differential Equations
 no no no no no 1067 Professor Long Fei feilonghd@yahoo.com.cn Hunan City University, Yiyang, Hunan, P. R. China
no no no no no 1074 Prof. Stevic S. sstevic@ptt.rs Mathematical Institute of the Serbian Academy of Sciences, Beograd, Serbia
ordinary differential and difference equations, functional differential equations and systems
 yes no no no no 1079 Dr. Bravyi E. bravyi@gmail.com Perm State Technical University, Perm, Russia
functional differential equations, boundary value problems
 no no no no no 1085 Professor Pan Yuanyuan pan_yuanyuan@163.com Jinan University, Jinan, P. R. China
no no no no no 1108 Professor Wang Da-Bin wangdb96@163.com Lanzhou University of Technology, Lanzhou, Gansu, P. R. China
no no no no no 1115 Prof. Xiao Ti-Jun xiaotj@ustc.edu.cn Fudan University, Shanghai, P. R. China
no no no no no 1126 Prof. Li Dingshi lidingshi2006@163.com Sichuan University, Chengdu, P. R. China
no no no no no 1127 Dr. Spadini M. marco.spadini@unifi.it Dipartimento di Sistemi e Informatica, Universita' di Firenze, Italy www.dma.unifi.it/~spadini
Topological methods in nonlinear analysis, ordinary differential equations on differentiable manifolds.
 no no no no no 1128 Prof. Bisconti L. luca.bisconti@unifi.it Dipartimento di Sistemi e Informatica, Universita' di Firenze, Italy
no no no no no 1131 dr Xu Jiafa xujiafa292@sina.com School of Mathematics, Shandong University, Jinan, Shandong, P. R. China
ordinary and partial differential equations, boundary value problems, spectral theory, operator theory, nonlinear functional analysis, fractional differential equations
 no no no no no 1132 Prof. Hakl R. hakl@ipm.cz Institute of Mathematics of the Academy of Sciences of Czech Republic, Branch in Brno http://www.math.muni.cz/index.html.en
no no no no no 1138 Prof. Cabada A. alberto.cabada@usc.es Universidad de Santiago de Compostela http://webspersoais.usc.es/persoais/alberto.cabada/
ordinary differential equations, difference equations, boundary value problems
 yes no no no no 1158 Prof. Lv Linli lvlinli2008@126.com Guizhou University, Guiyang, Guizhou, P. R. China
no no no no no 1160 Prof. Du Bo dubo7307@163.com Huaiyin Normal University, Huaiyin, Jiangsu, P. R. China
no no no no no 1173 Prof. Sathya R. sathyain.math@gmail.com Bharathiar University, Coimbatore, India
no no no no no 1177 Professor Guo Yingxin yxguo312@163.com Qufu Normal University, Qufu, P. R. China
no no no no no 1187 Dr. Liu Bingchen bcliu@aliyun.com College of Sciences, China University of Petroleum,Qingdao, Shandong, P. R. China
Partial Differential Equation
 no no no no no 1188 Prof. Li Fengjie fjlbcl@yahoo.com.cn College of Sciences, China University of Petroleum,Qingdao, Shandong, P. R. China
no no no no no 1191 Prof. Zhu Gang zhugang@yahoo.cn Harbin Institute of Technology, Harbin, P. R. China
no no no no no 1207 Dr. Moussaoui T. moussaoui@ens-kouba.dz ENS, Lab. EDP & HM, Kouba, Algiers, Algeria
no no no no no 1214 Prof. Hassan T. S. tshassan@mans.edu.eg Mansoura University, Mansoura, Egypt
no no no no no 1215 Prof. Wang Xuhuan wangxuhuan85@yahoo.cn Department of Mathematics, Baoshan College, Baoshan, Yunnan 678000, P. R. China
no no no no no 1218 Prof. Shahzad N. nshahzad@kau.edu.sa King Abdulaziz University, Jeddah, Saudi Arabia
Fixed point theory and its applications
 no no no no no 1219 Prof. Pathak H. K. hkpathak05@gmail.com Pt. Ravishankar Shukla University, Raipur, India
no no no no no 1232 Prof. Cheng Sui Sun sscheng@math.nthu.edu.tw Tsing Hua University, Hsinchu, Taiwan
no no no no no 1240 Prof. Liu Kai liukai418@126.com Nanchang University, Nanchang, P. R. China
no no no no no 1256 Prof. Medved M. Milan.Medved@fmph.uniba.sk Comenius University, Bratislava, Slovakia http://hore.dnom.fmph.uniba.sk
Differential equations, dynamical systems, bifurcation theory, control theory,
integral inequalities, evolution equations
 no no no no no 1259 mr. Ladics T. tamas.ladics@gmail.com Szent István University, Budapest, Hungary
Operator splitting, partial differential equations, numerical methods
 no no no no no 1263 Prof. Zhang Hai-E haiezhang@126.com Tangshan College, Tangshan, Hebei, P. R. China
no no no no no 1274 Prof. Liu Bo liubom@jlu.edu.cn College of Mathematics, Jilin University, P. R. China
no no no no no 1276 Prof. Tao Qiang taoq060@nenu.edu.cn School of Mathematics and Statistics, Northeast Normal University, Changchun, P. R. China
no no no no no 1277 Prof. Gao Hang hangg@nenu.edu.cn School of Mathematics & Statistics, Northeast Normal University, Changchun, P. R. China
no no no no no 1278 Prof. Cheng Jian jian.cheng2@mail.dcu.ie School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland
Asymptotic behaviour of solutions of differential equations with fading perturbations.
 no no no no no 1281 dr. Zemanek P. zemanekp@math.muni.cz Masaryk University, Brno, Czech Republic
no no no no no 1282 Prof. Simon Hilscher R. hilscher@math.muni.cz Masaryk University, Brno, Czech Republic
no no no no no 1285 Prof. Krejčová J. krejcovajana@mail.muni.cz Masaryk University, Brno, Czech Republic
no no no no no 1294 Prof. Saierli O. saierli_olivia@yahoo.com West University of Timisoara, Timisoara, Romania
no no no no no 1296 Prof. Sun Bo sunbo19830328@163.com Central University of Finance and Economics, Beijing, P. R. China
no no no no no 1301 Dr. Lai Mijia yjmlai@gmail.com University of Iowa, Iowa City, IA, U.S.A.
Partial differential equations
 no no no no no 1302 Prof. Yao Fengping fengpingyao@gmail.com Shanghai University, Shanghai, P. R. China
no no no no no 1303 Prof. Jia Huilian jiahl@mail.xjtu.edu.cn Xian Jiaotong University, Xian, P. R. China
no no no no no 1306 dr. Guo Zhichang mathgzc@gmail.com Harbin Institute of Technology, Harbin, P. R. China
nonlinear diffusion equation, image processing
 no no no no no 1311 Prof. Rui Wenjuan wenjuanrui@126.com China University of Mining and Technology, Xuzhou, P.R. China
Existence of solutions of differential equations of fractional order
 no no no no no 1312 Prof. Reznickova J. reznickova@fai.utb.cz Tomas Bata University, Zlin, Czech Republic
no no no no no 1314 prof Khodja B. brahim.khodja@univ-annaba.org Badji Mokhtar University, Annaba, Algeria
elliptic partial differential equations, ordinary differential equations
 no no no no no 1315 Prof. Tian Junkang tianjunkang1980@163.com University of Electronic Science and Technology, Chengdu, Sichuan, P. R. China
no no no no no 1316 Dr. Gamliel D. dang@ariel.ac.il Ariel University Center of Samaria, Israel
medical physics, specifically MRI (magnetic resonance imaging) and also NMR (nuclear magnetic resonance)
 no no no no no 1321 Dr. Ronto A. ronto@math.cas.cz Institute of Mathematics AV CR, Brno, Czech Republic
Differential equations
 no no no no no 1322 Prof. Petrusel A. petrusel@math.ubbcluj.ro Department of Applied Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
no no no no no 1324 Prof. Domoshnitsky A. adom@ariel.ac.il Ariel University Center of Samaria, Ariel, Israel http://www.ariel.ac.il/Projects/dom/al/ken.htm
theory of functional differential equations, boundary value problems, positivity of solutions, nonoscillation, stability, integro-differential equations, impulsive equations
 no no no no no 1325 Prof. Maghakyan A. mabrham@walla.com Bar Ilan University, Ramat Gan, Israel
no no no no no 1326 Prof. Yanetz S. yanetz@math.biu.ac.il Bar Ilan University, Ramat Gan, Israel
no no no no no 1327 dr. Veselý M. michal.vesely@mail.muni.cz Masaryk University, Brno, Czech Republic
no no no no no 1328 Prof. Hasil P. hasil@mendelu.cz Mendel University in Brno, Brno, Czech Republic
no no no no no 1331 Dr. Kennedy Benjamin B. bkennedy@gettysburg.edu Gettysburg College, Gettysburg, PA, U.S.A.
Differential delay equations
 no no no no no 1337 Prof Li Fengquan fqli@dlut.edu.cn Dalian University of Technology, Dalian, Liaoning, P. R. China
Partial differential equations
 no no no no no 1338 Prof. Lv Boqiang lbq86@yahoo.com.cn Nanchang Hangkong University, Nanchang, P. R. China
no no no no no 1339 Prof. Zou Weilin zwl267@yahoo.com.cn Nanchang Hangkong University, Nanchang, P. R. China
no no no no no 1340 Prof. Röst G. rost@math.u-szeged.hu Bolyai Institute, University of Szeged, Hungary http://www.epidelay.u-szeged.hu
delay differential equations, modeling of infectious diseases
 yes no no no no 1342 Prof. Mincsovics M. mincso@cs.elte.hu L. Eötvös University, Budapest, Hungary
no no no no no 1351 Prof. Zeidan V. zeidan@math.msu.edu Michigan State University, East Lansing, MI, U.S.A.
no no no no no 1355 Prof. Diblik J. diblik@feec.vutbr.cz Brno University of Technology, Brno, Czech Republic http://www.vutbr.cz/en/people/josef-diblik-1492
qualitative and quantitative properties of solutions of ordinary differential and difference equations
yes no no no no 1356 Professor Sugie J. jsugie@riko.shimane-u.ac.jp Shimane University, Matsue, Japan
ordinary differential equations, Lienard dynamical system, oscillation theory, qualitative theory, stability theory
 yes no no no no 1358 Prof. Xu Shenghu xuluck2001@163.com Longdong University, Qingyang, Gansu, P. R. China
no no no no no 1370 Prof. Fu Yongqiang fuyqhagd@yahoo.cn Harbin Institute of Technology, Harbin, P. R. China
Functional Analysis, Partial Differential Equations
 no no no no no 1371 Prof. Xiang Mingqi colfuyq@qq.com Harbin Institute of Technology, Harbin, P. R. China
no no no no no 1372 Prof. Pan Ning hljpning@yahoo.cn Northeast Forestry University, Harbin, P. R. China
no no no no no 1375 Prof. Abbas S. abbasmsaid@yahoo.fr University of Saida, Saida, Algérie
no no no no no 1377 prof. Belaidi B. belaidibenharrat@yahoo.fr University of Mostaganem, Mostaganem, Algeria http://www.univ-mosta.dz/
Complex differential equations, value distribution theory
 no no no no no 1378 Prof. Habib H. h.habib_maths@yahoo.fr University of Mostaganem, Mostaganem, Algeria
no no no no no 1383 Prof. Zhang Huixing huixingzhangcumt@163.com China University of Technology and Mining, Xuzhou City, Jiangsu, P. R. China
Partial Differential Equations
 no no no no no 1386 Prof. Zhang Liang 32278592@qq.com Northwest A & F University, Yangling, Shaanxi, P. R. China
no no no no no 1388 Dr. Zhou Xueyong xueyongzhou@126.com College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, Henan, P.R. China
Dynamical Systems,
Mathematical Biology,
Epidemiology
no no no no no 1389 Professor Diamandescu A. adiamandescu@rdslink.ro University of Craiova, Craiova, Romania
no no no no no 1390 Professor Sun Yuangong ss_sunyg@ujn.edu.cn School of Mathematics, University of Jinan, Shandong, P. R. China
no no no no no 1396 Prof. Zhang Shuqin zsqjk@163.com China University of Mining and Technology, Beijing, China
no no no no no 1398 Prof. Wang Zhengmei zhengmeiwang@126.com Wuhan University of Technology, Wuhan, Hubei, P. R. China
no no no no no 1410 dr Zhou Jun jzhou@swu.edu.cn Southwest University, Chongqing, P. R. China
no no no no no 1412 Prof. Grace Said R. saidgrace@yahoo.com Cairo University, Orman, Giza, Egypt
no no no no no 1421 Dr. Heidarkhani Shapour s.heidarkhani@razi.ac.ir Razi University, Kermanshah, Iran
no no no no no 1425 Professor Agarwal Ravi P. agarwal@tamuk.edu Texas A&M University-Kingsville, Kingsville, TX, USA
Nonlinear Analysis
 no no no no no 1438 Prof Mesloub Said mesloubs@yahoo.com King Saud University, Riyadh, Saudi Arabia
partial differential equations, evolutions equations (parabolic, hyperbolic), boundary value problems, analysis, applied math.
 no no no no no 1445 Dr. Dilna N. natalia.dilna@zoznam.sk Mathematical Institute, Slovak Academy of
 Sciences, Bratislava, 
Slovakia http://www.mat.savba.sk/~dilna
functional differential equations, boundary value problems
 no no no no no 1451 Dr. Wang Qing q7wang@gmail.com Shepherd University, Shepherdstown, WV, U.S.A.
Stability of (impulsive) delay differential equations and applications
no no no no no 1452 Prof. Zhu Quanxin zqx22@126.com Ningbo University, Ningbo, Zhejiang, P. R. China
no no no no no 1455 Prof. Liu Xinzhi xzliu@uwaterloo.ca University of Waterloo, Ontario, Canada http://monotone.uwaterloo.ca/~journal/Liu.htm
Differential equations
 no no no no no 1457 Prof. Liang Jitai jitailiang@gmail.com Yunnan Normal University Business School, Kunming, Yunnan, P.R. China
no no no no no 1462 Prof. Zhang Chao ss_zhangc@ujn.edu.cn University of Jinan, Jinan, Shandong, P. R. China
no no no no no 1471 Prof. Boukhatem Yamna byamna@yahoo.fr Departement of Mathematics, Setif university, Algeria
nonlinear boundary value problem, semilinear hyperbolic equations
 no no no no no 1484 Prof. Rehak P. rehak@math.cas.cz Academy of Sciences of the Czech Republic, Brno, Czech Republic http://www.math.muni.cz/kma.html.en
no no no no no 1488 Professor Wang Min min-wang@utc.edu University of Tennessee at Chattanooga, Chattanooga, TN, U.S.A.
Nonlinear boundary value problems for ordinary differential equations and difference equations; stability of functional differential equations.
no no no no no 1489 Prof. Yang Li yang@yahoo.com Liaoning University, Liaoning, P. R. China
no no no no no 1490 Prof. Zhang Zhigang zgz@123.com Hubei University, Wuhan, P. R. China
no no no no no 1498 Professor Chen Haibo hbchen2003@gmail.com Central South University, Changsha, Hunan, P. R. China
no no no no no 1505 Prof. Jiang Jiqiang qfjjq@163.com School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, P. R. of China
Ordinary differential equations
 no no no no no 1518 Prof. Sreedhar N. sreedharnamburi@rediffmail.com GITAM University, Visakhapatnam, India
no no no no no 1526 Prof. Wang Weihua wangvh@163.com Putian University, Fujian, P. R. China
no no no no no 1530 Dr. Dabas J. jay.dabas@gmail.com IIT Roorkee, Saharanpur Campus, Saharanpur, India
Differential Equations, Fractional Differential Equations, Impulsive Differential Equations, Method of Lines
 no no no no no 1535 dr Ding Youzheng dingyouzheng@163.com Shandong Jianzhu University, Jinan, Shandong, P. R. China
spectral theory, operator theory, boundary value problem of ODE, nonlinear analysis, fractional differential equations
 no no no no no 1548 Prof. Chen Yuan-Yuan 792425475@qq.com Jiangxi Normal University, Nanchang, Jiangxi, P. R. China
no no no no no 1549 Dr. Neugebauer J. T. jeffrey.neugebauer@eku.edu Eastern Kentucky University, Richmond, KY, U.S.A.
ordinary differential equations
 no no no no no 1551 Prof. Zhang Zhengce zhangzc@mail.xjtu.edu.cn Xi'an Jiaotong University, Xi'an, P. R. China
PDE
 no no no no no 1569 Professor Wang Zejia matwzj@jlu.edu.cn Jilin University, Changchun, P. R. China
no no no no no 1573 Prof. Duan Lian duanlianjx2012@yahoo.cn Jiaxing University, Jiaxing, Zhejiang, P. R. China
Coincide degree and nonlinear differential equations, Delay Differential Equations with Applications in Population Dynamics
 no no no no no 1574 Prof. Hou Xinhua xinhuahou@yahoo.cn Hunan Industry Polytechnic, Changsha, Hunan, P. R. China
no no no no no 1576 Prof. Tanaka Satoshi tanaka@xmath.ous.ac.jp Okayama University of Science, Okayama, Japan
no no no no no 1589 Prof. Benabderrahmane Benyattou bbenyattou@yahoo.com Laboratory of Mathematics and Computer Sciences, University of Laghouat, Algeria
Applied Mathematics, PDE
 no no no no no 1593 Prof. Wu Yonghong yhwu@maths.curtin.edu.au Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia
no no no no no 1594 Prof. Benmezai A. abenmezai@yahoo.fr Faculty of Mathematics, USTHB, Algeirs, Algeria
Boundary value problems, Fixed point theory, Differential equations.
 no no no no no 1596 Prof. Meng Junxia mengjunxia1968@yahoo.com.cn College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejian, P. R. China
coincide degree and nonlinear differential equations, delay differential equations with applications in population dynamics
 no no no no no 1609 Prof. Huang Huang-Nan nhuang@thu.edu.tw Tunghai University, Taichung, Taiwan
numerical computation, functional differential equation, optimal control, mathematical control theory, Stefan problem, spectral interpolation problem
 no no no no no 1610 Asst. Prof. Lin Che-Hao linch@thu.edu.tw Tunghai University, Taichung, Taiwan
differential equations, dynamical systems
 no no no no no 1611 Prof. Ho Chao-Pao cpho@thu.edu.tw Tunghai University, Taichung, Taiwan
no no no no no 1627 Prof. Skripkova L. lucia.skripkova@fmph.uniba.sk Comenius University, Bratislava, Slovakia
no no no no no 1638 Prof. Lazar V. L. vasilazar@yahoo.com "Vasile Goldis" Western University Arad, Satu Mare, Romania
ODE and PDE, Fixed Point Theory, Option pricing
no no no no no 1642 Prof. Zhang Xiaozhi xzzhang@yahoo.com.cn Nanchang University, Nanchang, Jiangxi, P. R. China
fractional differential equations;
Bound value problem
 no no no no no 1643 Prof. Zhu Chuanxi chuanxizhu@126.com Nanchang University, Nanchang, Jiangxi, P. R. China
no no no no no 1644 Prof. Rebey A. rebey_amor@yahoo.fr Institut Supérieur des Mathématiques Appliquées, Kairouan, Tunisia
no no no no no 1661 Prof. Franca Matteo franca@dipmat.univpm.it Università Politecnica delle Marche, Ancona, Italy
no no no no no 1689 Prof. Obaidat S. saleem@ksu.edu.sa King Saud University, Riyadh, Saudi Arabia
no no no no no 1699 Prof. Cui Yujun cyj720201@163.com Shandong University of Science and Technology, Qingdao, Shandong, P. R. China
Nonlinear functional analysis
 no no no no no 1702 dr Shoukaku Yutaka shoukaku@t.kanazawa-u.ac.jp Kanazawa University, Kanazawa, Japan
partial differential equations, oscillation theorem
 no no no no no 1703 Prof. Yoshida Norio nori@sci.u-toyama.ac.jp University of Toyama, Toyama, Japan
no no no no no 1730 Prof. Liu Jie jliulut@163.com Lanzhou University of Technology, Lanzhou, Gansu, P. R. China
no no no no no 1733 Prof. Zheng Xiong-Jun xjzh1985@126.com Jiangxi Normal University, Nanchang, Jiangxi, P. R. China
no no no no no 1734 Prof. Li Lu 181793361@qq.com Jiangxi Normal University, Nanchang, Jiangxi, P. R. China
no no no no no 1738 Prof. Liu Xueyan xueyan_liu@baylor.edu Department of Mathematics, Baylor University, Waco, TX, U.S.A.
no no no no no 1746 Prof. Xiao Lipeng lipeng_xiao08@yahoo.com Institute of Mathematics and Informations, Jiangxi Normal University, Nanchang, P. R. China
no no no no no 1763 prof. Manojlović Jelena jelenam@pmf.ni.ac.rs University of Nis, Nis, Serbia http://www.pmf.ni.ac.yu
Ordinary differential equations: oscillation theory, asymptotic analysis, qualitative analysis
 no no no no no 1764 Prof. Kusano Takasi kusanot@zj8.so-net.ne.jp Hiroshima University, Higashi-Hiroshima, Japan
no no no no no 1768 Prof. El Moumni Mostafa mostafaelmoumni@gmail.com Department of Mathematics, University Sidi Mohamed Ben Abdellah, Fez, Morocco
no no no no no 1773 Professor Ospanov Kordan Nauryzkhanovich kordan.ospanov@gmail.com L. N. Gumilyev Eurasian National University, Kazakhstan
Mathematica, Differential Equations, Singular Differential Equations
 no no no no no 1778 Prof. Liu Yuji liuyuji888@sohu.com Guangdong University of Business Studies, Guangzhou, P. R. China
Differential equations
 no no no no no 1794 Prof. Zhuang Rong-Kun rkzhuang@163.com Department of Mathematics, Huizhou University, Huizhou, P. R. China
no no no no no 1795 Prof. Zhu Liping ny.zlp@stu.xjtu.edu.cn Xi'an University of Architecture & Technology, Xi'an, P. R. China
no no no no no 1796 Prof. Aliziane T. taliziane@gmail.com University of Sciences and Technology Houari Boumediene, Algiers, Algeria
PDE, Degenerate equations, Reaction Diffusion Systems, Control, stabilisation.
 no no no no no 1807 Ph.D Wu Xiaotai aaxtwu@gmail.com Anhui Polytechnic University, Wuhu, Anhui, P.R. China
stochastic differential equation, stability of stochastic systems
 no no no no no 1808 Prof. Yan Litan ylwu@ahpu.edu.cn Donghua University, Shanghai, P. R. China
no no no no no 1816 Prof. Dai Guowei daiguowei@nwnu.edu.cn Department of Mathematics, Lanzhou University, Lanzhou, P. R. China
no no no no no 1822 Prof. Boutana I. bou.imen@yahoo.fr Université de Jijel, Jijel, Algérie
no no no no no 1823 Prof. Makhlouf A. amira.makhlouf18@gmail.com Université de jijel, Jijel, Algérie
no no no no no 1835 Prof. Deboli A. adeboli@dm.uba.ar Universidad de Buenos Aires, Buenos Aires, Argentina
no no no no no 1869 Prof. Akhmetkaliyeva Raya Duisenbekovna raya.84@mail.ru L. N. Gumilyev Eurasian National University, Kazakhstan
no no no no no 1871 Prof. Duan Ning 123332453@qq.com College of Mathematics, Jilin University, P. R. China
no no no no no 1888 Dr Chen De-Han dhchern@sina.com Nanchang University, Nanchang, Jiangxi, P.R. China
abstract evolution equations, partial differential equations, operator theory
 no no no no no 1898 Prof. Wu Zhaoqi wuzhaoqi_conquer@163.com Nanchang University, Nanchang, Jiangxi, P. R. China
no no no no no 1901 Prof. Luca R. rluca@math.tuiasi.ro Gh. Asachi Technical University, Iasi, Romania
ordinary differential equations, partial differential equations, difference equations
 no no no no no 1908 Dr. Li Bing libingcnjy@163.com College of Science, Chongqing Jiaotong University, Chongqing, P. R. China
functional differential equation, stability theory
 no no no no no 1917 Prof. Ye Haiping hpye@dhu.edu.cn Department of Applied Mathematics, Donghua University, Shanghai, P. R. China
fractional differential equations
 no no no no no 1920 Prof. Liu Jiao lh100986@163.com Department of Applied Mathematics, Donghua University, Shanghai, P. R. China
no no no no no 1921 Prof. Gao Jianming jmgao@dhu.edu.cn Department of Applied Mathematics, Donghua University, Shanghai, P. R. China
no no no no no 1926 Prof. Jiang Weihua weihuajiang@hebust.edu.cn Hebei University of Science and Technology, Hebei, P. R. China
ordinary differential equations
 no no no no no 1932 Prof. Lizama Carlos carlos.lizama@usach.cl Universidad de Santiago de Chile, Santiago, Chile
qualitative theory of evolution equations
 no no no no no 1944 Prof. Araya Daniela daniela.araya@uss.cl Universidad San Sebastian, Santiago, Chile
no no no no no 1946 Prof. Zhang Qiang zq7718@126.com Hebei University of Science and Technology, Hebei, P. R. China
no no no no no 1947 Prof. Guo Weiwei gww0222@126.com Hebei University of Science and Technology, Hebei, P. R. China
no no no no no 1957 Prof. Shao Jianying shaojianying2008@yahoo.cn Jiaxing University, Jiaxing, Zhejiang, P. R. China
periodic solutions of nonlinear differential equations
no no no no no 1958 Prof. Jiang Ani jiangani@yahoo.cn Hunan University of Arts and Science, Changde, Hunan, P. R. China
no no no no no 1963 Dr. Nápoles Valdes Juan Eduardo jnapoles@exa.unne.edu.ar UNNE, FaCENA, Corrientes, Argentina
boundedness, periodicity, stability
 no no no no no 1965 Dr. Al-Refai Mohammed m_alrefai@uaeu.ac.ae Dept. of Mathematical Sciences, UAE University, Al Ain, UAE
fractional Calculus, maximum principle, partial differential equations
 no no no no no 1995 Prof. Marynets Kateryna katya_marinets@ukr.net Uzhgorod National University, Uzhgorod, Ukraine
no no no no no 1996 Prof. Chen Wei chenweiwang2009@yahoo.com.cn Shanghai Lixin University of Commerce, Shanghai, P. R. China
monotone dynamic systems, qualitative theory of differential equations and difference equations, computer-aided geometric design
 no no no no no 2014 Prof. Pospíšil Michal michal.pospisil@mat.savba.sk Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia
no no no no no 2022 Prof. Chatzarakis George E. gea.xatz@aspete.gr Department of Electrical Engineering Educators, Athens, Greece
no no no no no 2029 Prof. Ma Suang-Hong mashuanghong@lut.cn Lanzhou University of Technology, Lanzhou, Gansu, P. R. China
no no no no no 2032 Professor Shi Shaoyun shisy@jlu.edu.cn College of Mathematics, Jilin University, Changchun, P. R. China
no no no no no 2051 Prof. Guo Zhen xytcgz2002@sohu.com Xinyang Normal University, Xinyang, P. R. China
no no no no no 2061 Prof. Wang Tingxiu twang1@missouriwestern.edu Missouri Western State University, Saint Joseph, MO, U.S.A.
no no no no no 2063 Prof. Assolami Afrah af-rah1@hotmail.com King Abdulaziz University, Jeddah, Saudi Arabia
no no no no no 2069 Prof. Dubickas Arturas arturas.dubickas@mif.vu.lt Department of Mathematics and Informatics and Institute of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania
no no no no no 2073 Prof. Li Fang-lan lifl80@yahoo.com.cn Shanghai Medical Instrumentation College, Shanghai, P. R. China
no no no no no 2083 Prof. Ye Yuan yye_yd@yahoo.com.cn Yunnan University, Kunming, Yunnan, P. R. China
no no no no no 2089 dr Wang Zhao wangzhao2717@163.com Department of Mathematics, Jilin University, Changchun, China http://www.jlu.edu.cn/
no no no no no 2105 Prof. Chen Zhibin chenzhibinbin@yahoo.cn Hunan University of Technology, Hunan, Zhuzhou, P. R. China
dynamics of nonlinear differential equations
 no no no no no 2112 Prof. Chakrone Omar chakrone@yahoo.fr University Mohamed Ist, Oujda, Morocco http://www.univ-oujda.ac.ma/
no no no no no 2126 Prof. Rama Renu renurama68@gmail.com Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India
no no no no no 2127 dr. Kostic Marko marco.s@verat.net Faculty of Technical Sciences, Novi Sad, Serbia
operator theory, abstract Volterra equations
 no no no no no 2133 Prof. Puriuskis Gintaras gintaras.puriuskis@maf.vu.lt Department of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania
no no no no no 2135 Dr. Miao Chunmei mathchunmei2012@yahoo.cn College of Science, Changchun University, Changchun, P. R. China
boundary value problem, spectral theory
 no no no no no 2157 Prof. Wang Rong-Nian rnwong@163.com Nanchang University, Nanchang, Jiangxi, P.R. China
partial differential equations, dynamical systems, operator theory
 no no no no no 2179 Prof. Jaros Jaroslav jaros@fmph.uniba.sk Comenius University, Bratislava, Slovakia
half-linear differential equations, oscillation and nonoscillation of solutions, comparison, regular variation
 no no no no no 2180 Prof. Rachunkova Irena irena.rachunkova@upol.cz Palacky University, Olomouc, Czech Republic
no no no no no 2190 PhD student Louis-Rose Carole carole.louis-rose@hotmail.fr Laboratoire CEREGMIA, Université des Antilles et de la Guyane, Guadeloupe
partial differential equations, controllability
no no no no no 2198 Prof. Chen Chuanming chuanmingchen@hotmail.com Yunnan Normal University Business School, Kunming, Yunnan, P.R. China
no no no no no 2199 Prof. Zhen Boqian zhenboqian@163.com Yunnan Normal University Business School, Kunming, Yunnan, P.R. China
no no no no no 2227 Prof. Xu Yanli xuyanliling@yahoo.cn Xiangnan College, Chenzhou, Hunan, P. R. China
periodic differential equations, nonlinear dynamic systems, neural network dynamics
 no no no no no 2235 Prof. Bouziani Abdelfatah af_bouziani@hotmail.com Oum El Bouagui B.P. 565, 04000, Algérie.
no no no no no 2240 Prof. Zhang Tian-Wei-Tian zhang@kmust.edu.cn Kunming University of Science and Technology, Kunming, P. R. China
Nonlinear dynamic systems, neural networks, biomathematics and applied mathematics.
 no no no no no 2241 Prof Hattaf Khalid k.hattaf@yahoo.fr Faculty of Sciences Ben M’sik, Hassan II University, Casablanca, Morocco
ordinary and delay differential equations, mathematical biology and medicine, control theory, and dynamical systems
 no no no no no 2242 Prof. Lashari Abid Ali abidlshr@yahoo.com National University of Sciences and Technology, Islamabad, Pakistan
no no no no no 2243 Prof. Louartassi Younes y−louartassi@yahoo.fr Department of Electrical Engineering, Mohammadia School Engineering, Rabat, Morocco
no no no no no 2244 Prof. Yousfi Noura nourayousfi@gmail.com Faculty of Sciences Ben M’sik, Hassan II University, Casablanca, Morroco
no no no no no 2268 Prof. Lu Liang gxluliang@163.com College of Science, Guangxi University for Nationalities, Nanning, Guangxi, P. R. China
ordinary differential equations, boundary value problems, fractional differential equations
 no no no no no 2274 Prof. Petre I. R. ioan.petre@ubbcluj.ro Department of Applied Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
no no no no no 2276 Prof. Xiong Wanmin wanminxiong2009@yahoo.com.cn Furong College, Hunan University of Arts and Science, P.R. China
no no no no no 2278 Knipl Diana knipl@math.u-szeged.hu MTA-SZTE Analysis and Stochastics Research Group of the Hungarian Academy of Sciences Bolyai Institute, University of Szeged, Szeged, Hungary
no no no no no 2306 Dr. Zhang Xingyong zhangxingyong1@gmail.com Department of Mathematics, Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan, P. R. China
no no no no no 2308 Prof. Rubbioni Paola rubbioni@dmi.unipg.it Department of Mathematics and Informatics, University of Perugia, Perugia, Italy www.dmi.unipg.it/rubbioni
differential equations and inclusions, fixed point theory
 no no no no no 2313 dr. Li Nan lzyang@sdu.edu.cn Shandong University, Jinan, Shandong, P. R. China
no no no no no 2322 Prof. Cardinali Tiziana tiziana@dmi.unipg.it Department of Mathematics and Informatics, University of Perugia, Italy
no no no no no 2334 dr. Poulou Marilena N. mpoulou@math.ntua.gr National Technical University of Athens, Athens, Greece
dynamical systems
 no no no no no 2351 Prof. Tunc Ercan ercantunc72@yahoo.com Gaziosmanpasa University, Tokat, Turkey
no no no no no 2401 Prof. Youssfi Ahmed ahmed.youssfi@gmail.com Department of Mathematics, Moulay Ismail University, Errachidia, Morocco
Sobolev spaces, Orlicz-Sobolev spaces,PDE's: elliptic equations, unilateral problems, existence, uniqueness, regularity
no no no no no 2420 Prof. Molica Bisci Giovanni gmolica@unirc.it University of Reggio Calabria, Reggio Calabria, Italy
variational methods, critical point theory, difference equations, analysis on manifolds
 no no no no no 2421 Prof. D'Aguì Giuseppina dagui@unime.it University of Messina, Messina, Italy
no no no no no 2441 PhD Student Fekete I. feipaat@cs.elte.hu Department of Applied Analysis and Computational Mathematics Institute of Mathematics Faculty of Science Eötvös Loránd University Pázmány P. sétány 1/C H-1117 Budapest www.cs.elte.hu/~feipaat
Nonlinear Stability Theory
Ordinary Differential Equations
 no no no no no 2609 Prof. Ashyralyev A. aashyr@fatih.edu.tr Fatih University, Istanbul, Turkey http://math.fatih.edu.tr/?cv,202
Theory of Differential and Integral Inequalities and its Applications, Semigroups of Linear Operators and Their Applications to Partial Differential Equations, Theory of Positive Operators and Stability of Difference Schemes, Theory of Interpolation of Operators and its Applications, Difference Schemes for Stochastic Partial Differential Equations, Uniform Difference Schemes for Singular Perturbation Problems, Non-Classical Problems of Mathematical Physics, Well-Posedness of Parabolic and Elliptic Differential and Difference Equations, Stability of the Neutral Delay Differential and Difference Equations, Numerical Solving of Applied Problems, Reading, Taking Part in the Preparation of Secondary School and University Students for Mathematical Olympiads
no no no no no 2625 Prof. Cao Yang mathcy@dlut.edu.cn Dalian University of Technology, Dalian, P. R. China
no no no no no 2696 Prof. Yang Lianzhong nanli32787310@163.com Shandong University, Jinan, Shandong, P. R. China
no no no no no 2747 Prof. Dhage Bapurao C bcdhage@gmail.com Kasubai, Gurukul Colony, Ahmedpur, Maharashtra, India
Nonlinear Analysis
 no no no no no 6 1 1998 1 0 Marachkov type stability results for functional differential equations
This paper is concerned with systems of functional differential equations with either finite or infinite delay. We give conditions on the system and on a Liapunov function to ensure that the zero solution is asymptotically stable. The main result of this paper is that the assumption on boundedness in Marachkov type stability results may be replaced (in both the finite and the infinite delay case) with the condition that $|f(t,\varphi)|\le F(t)$ such that $\int^{\infty} 1/F(t) dt=\infty$.
 1 17 858 . .
1998-01-01 0000-00-00 857 yes 3 no 7 1 1998 2 0 On the asymptotic behavior of the pantograph equations
Our aim is studing the asymptotic behaviour of the solutions of the equation $\dot x(t) = -a(t)x(t)+a(t)x(pt)$ where $0<p<1$ is a constant. This equation is a special case of the so called pantograph equations of the form $\dot x(t) = -a(t)x(t)+b(t)x(p(t))$. First we prove an asymptotic estimate of the solutions of the later equation, then using this result we show the asymptotic behavior of the solutions of the former equation. In particular, we prove that all solutions are asymptotically logarithmically periodic.
1 12 857 . .
1998-01-01 0000-00-00 3 yes 26 no 8 1 1998 3 0 Almost periodic processes and the existence of almost periodic solutions
Some property which is equivalent to the concept of an asymptotically almost periodic integral for almost periodic processes is introduced. By using this property, it is shown that a precompact integral of almost periodic processes which is uniformly asymptotically stable is an asymptotically almost periodic integral. Results are applied to the existence of almost periodic solutions of some evolution equation.
1 19 6 . .
1998-01-01 0000-00-00 27 yes 867 no 9 1 1998 4 0 On the existence of almost periodic solutions of neutral functional differential equations
This paper discusses the existence of almost periodic solutions of neutral functional differential equations. Using a Liapunov function and the Razumikhin's technique, we obtain the existence, uniqueness and stability of almost periodic solutions.
1 9 23 . .
1998-01-01 0000-00-00 28 yes 29 no 30 no 10 1 1998 5 0 Oscillation in neutral partial functional differential equations and inequalities
We derive some sufficient conditions for certain classes of ordinary differential inequalities of neutral type with distributed delay not to have eventually positive or negative solutions. These, together with the technique of spatial average, the Green's Theorem and Jensen's inequality, yield some sufficient conditions for all solutions of a class of neutral partial functional differential equations to be oscillatory. An example is given to illustrate the result.
1 14 25 . .
1998-01-01 0000-00-00 31 yes 23 no 11 1 1998 6 0 Existence of positive solutions for boundary value problem of second-order functional differential equation
We use a fixed point index theorem in cones to study the existence of positive solutions for boundary value problems of second-order functional differential equations of the form $$\left\{ \begin{array}{ll} y''(x)+r(x)f(y(w(x)))=0,&0<x<1,\\ \alpha y(x)-\beta y'(x)=\xi (x),&a\leq x\leq 0,\\ \gamma y(x)+\delta y'(x)=\eta (x),&1\leq x\leq b; \end{array}\right.$$ where $w(x)$ is a continuous function defined on $[0,1]$ and $r(x)$ is allowed to have singularities on $[0,1]$. The result here is the generalization of a corresponding result for ordinary differential equations.
1 13 25 . .
1998-01-01 0000-00-00 32 yes 33 no 12 1 1998 7 0 Asymptotic behavior of solutions to a quasilinear hyperbolic equation with nonlinear damping
We prove the existence and uniqueness of a global solution of a damped quasilinear hyperbolic equation. Key point to our proof is the use of the Yosida approximation. Furthermore, we apply a method based on a specific integral inequality to prove that the solution decays exponentially to zero when the time t goes to infinity.
1 12 858 . .
1998-01-01 0000-00-00 34 yes 13 1 1998 8 0 On the sign definiteness of Liapunov functionals and stability of a linear delay equation
In this paper we give a new definition of the positive-definiteness of the Liapunov functional involved in the stability and asymptotic stability investigation. Using this notion we prove Liapunov type theorems and apply these results to the scalar equation $\dot x(t)=b(t)x(t-r(t))$, where $b(t)$ and $r(t)$ may be unbounded.
 1 13 858 . .
1998-01-01 0000-00-00 35 yes 36 no 14 1 1998 9 0 Exact controllability of a second order integro-differential equation with a pressure term
This paper is concerned with the boundary exact controllability of the equation $$u''-\Delta u-\int_0^t g(t-\sigma)\Delta u(\sigma) d\sigma=-\nabla p$$ where $Q$ is a finite cilinder $\Omega\times]0,T[$, $\Omega$ is a bounded domain of $R^n$, $u=(u_1(x,t),\ldots,u_n(x,t))$, $x=(x_1,\ldots,x_n)$ are $n$-dimensional vectors and $p$ denotes the pressure term. The result is obtained by applying HUM (Hilbert Uniqueness Method) due to J. L. Lions. The above equation is a simple model of dynamical elasticity equations for incompressible materials with memory.
1 18 3 . .
1998-01-01 0000-00-00 37 yes 38 no 40 no 39 no 4 1 1999 1 0 On a spectral criterion for almost periodicity of solutions of periodic evolution equations
This paper is concerned with equations of the form: $u'=A(t)u + f(t)$, where $A(t)$ is (unbounded) periodic linear operator and f is almost periodic. We extend a central result on the spectral criteria for almost periodicity of solutions of evolution equations to some classes of periodic equations which says that if $u$ is a bounded uniformly continuous mild solution and $P$ is the monodromy operator, then their spectra satisfy $e^{i sp_{AP(u)}}\subset \sigma(P)\cap S^1$, where $S^1$ is the unit circle. This result is then applied to find almost periodic solutions to the above­mentioned equations. In particular, parabolic and functional differential equations are considered. Existence conditions for almost periodic and quasi­periodic solutions are discussed.
1 28 857 . .
1999-01-01 0000-00-00 41 yes 42 no 43 no 5 1 1999 2 0 Periodic solutions of semilinear equations at resonance with a $2n$-dimensional kernel
In this paper, we obtain some sufficient conditions for the existence of $2\pi$-periodic solutions of some semilinear equations at resonance where the kernel of the linear part has dimension $2n(n\ge 1)$. Our technique essentially bases on the Brouwer degree theory and Mawhin's coincidence degree theory.
1 13 867 . .
1999-01-01 0000-00-00 44 yes 29 no 3 1 1999 3 0 Nonexistense of global solutions of a quasilinear bi-hyperbolic equation with dynamical boundary conditions
In this work, the nonexistence of the global solutions to a class of initial boundary value problems with dissipative terms in the boundary conditions is considered for a quasilinear system of equations. The nonexistence proof is achieved by the use of a lemma due to O. Ladyzhenskaya and V.K. Kalantarov and by the usage of the so called generalized convexity method. In this method one writes down a functional which reflects the properties of dissipative boundary conditions and represents the norm of the solution in some sense, then proves that this functional satisfies the hypotheses of Ladyzhenskaya-Kalantarov lemma. Hence from the conclusion of the lemma one deduces that in a finite time $t_2$, this functional and hence the norm of the solution blows up.
1 10 3 . .
1999-01-01 0000-00-00 45 yes 46 no 2 1 1999 4 0 Hysteresis in Urysohn-Volterra systems
This paper deals with the hysteresis operator coupled to the system of Urysohn-Volterra equations. The local solutions of the system as well as the global solutions have been obtained.
1 8 5 . .
1999-01-01 0000-00-00 47 yes 1 1 1999 5 0 On nonnegative solutions of nonlinear two-point boundary value problems for two-dimensional differential systems with advanced arguments
In this paper we consider the differential system (1.1)
$u_i'(t)=f_i\big(t,u_1(\tau_{i1}(t)),u_2(\tau_{i2}(t))\big) (i=1,2)$
with the boundary conditions (1.2)
$\varphi\big(u_1(0),u_2(0)\big)=0, u_1(t)=u_1(a), u_2(t)=0 for t\geq a,$
where $f_i: [0,a]\times \Bbb{R}^2\to \Bbb{R}$ $(i=1,2)$ satisfy the local Carath\'{e}odory conditions, while $\varphi: \Bbb{R}^2\to \Bbb{R}$ and $\tau_{ik}: [0,a]\to [0,+\infty[$ $(i,k=1,2)$ are continuous functions. The optimal, in a certain sense, sufficient conditions are obtained for the existence and uniqueness of a nonnegative solution of the problem (1.1), (1.2).
 1 22 858 . .
1999-01-01 0000-00-00 11 yes 48 no 15 1 1999 6 0 A memory type boundary stabilization of a mildly damped wave equation
We consider the wave equation with a mild internal dissipation. It is proved that any small dissipation inside the domain is sufficient to uniformly stabilize the solution of this equation by means of a nonlinear feedback of memory type acting on a part of the boundary. This is established without any restriction on the space dimension and without geometrical conditions on the domain or its boundary.
 1 7 19 . .
1999-01-01 0000-00-00 55 yes 828 no 16 1 1999 7 0 Eigenvalue approximations for linear periodic differential equations with a singularity
We consider the second order, linear differential equation
$$y''(x) + (\lambda.q(x)) y(x) = 0 \eqno{(1)}$$
where $q$ is a real-valued, periodic function with period a. Our object in this paper is to derive asymptotic estimates for the eigenvalues of (1) on $[0;a]$ with periodic and semi­periodic boundary conditions. Our approach to regularizing (1) follows that used by Atkinson [1], Everitt and Race [4], and Harris and Race [6]. We illustrate our methods by calculating asymptotic estimates for the periodic and semi­periodic eigenvalues of (1) in the case where $q(x) = 1/|1-x|$.
 1 18 1455 . .
1999-01-01 0000-00-00 53 yes 54 no 17 1 1999 8 0 Exact multiplicity of positive solutions for a class of semilinear equations on a ball
We study exact multiplicity of positive solutions for a class of Dirichlet problems on a ball. We consider nonlinearities generalizing cubic, allowing both $f(0)=0$ and non-positone cases. We use bifurcation approach. We first prove our results for a special case, and then show that the global picture persists as we vary the roots.
 1 15 24 . .
1999-01-01 0000-00-00 51 yes 18 1 1999 9 0 Existence of stable periodic solutions of a semilinear parabolic problem under Hammerstein-type conditions
We prove the solvability of the parabolic problem
$$\partial_t u-\sum_{i,j=1}^N \partial_{x_i}(a_{i,j}(x,t)\partial_{x_j}u)+\sum_{i=1}^N b_i(x,t)\partial_{x_i}u=f(x,t,u)\hbox{ in }\Omega\times R$$
$$u(x,t)=0\hbox{ on }\partial\Omega\times R$$
$$u(x,t)=u(x,t+T)\hbox{ in }\Omega\times R$$
assuming certain conditions on the ratio $2\int_0^s f(x,t,\sigma) d\sigma/s^2$ with respect to the principal eigenvalue of the associated linear problem. The method of proof, whcih is based on the construction of upper and lower solutions, also yields information on the localization and the stability of the solution.
 1 24 24 . .
1999-01-01 0000-00-00 50 yes 49 no 19 1 1999 10 0 On some boundary value problems for systems of linear functional differential equations
In this paper on the segment $I=[a,b]$ we will consider the system of linear functional differential equations
\begin{equation}\label{1}
x'_i(t)=\sum\limits_{k=1}^n\ell_{ik}(x_k)(t)+q_i(t)\qquad (i=1,\dots,n)
\end{equation}
and its particular case
$$x'_i(t)=\sum\limits_{k=1}^n p_{ik}(t)x_k(\tau_{ik}(t))+q_i(t)\qquad (i=1,\dots,n)\eqno{(1')}$$
with the boundary conditions
\begin{equation}\label{2}
\int_a^b x_i(t)d\varphi_i(t)=c_i\qquad (i=1,\dots,n).
\end{equation}
Here $\ell_{ik}:C(I;\Bbb R)\to L(I;\Bbb R)$ are linear bounded operators, $p_{ik}$ and $q_i\in L(I;\Bbb R)$, $c_i\in\Bbb R$ $(i,k=1,\dots,n)$, $\varphi_i:I\to\Bbb R$ $(i=1,\dots,n)$ are the functions with bounded variations, and $\tau_{ik}:I\to I$ $(i,k=1,\dots,n)$ are measurable functions. The optimal, in some sense, conditions of unique solvability of the problems $(\ref{1})$, $(\ref{2})$ and $(1')$, $(\ref{2})$ are established.
 1 16 11 . .
1999-01-01 0000-00-00 1132 yes 24 1 1999 11 0 Global solutions for a nonlinear wave equation with the p-laplacian operator
We study the existence and asymptotic behavior of the global solutions of the nonlinear equation
$$u_tt-\Delta_p u+(-\Delta)^\alpha u_t+g(u)=f$$
where $0<alpha\leq 1$ and $g$ does not satisfy the sign condition $g(u)u \geq 0$.
 1 13 25 . .
1999-01-01 0000-00-00 65 yes 64 no 22 1 1999 12 0 Eigenvalue characterization for a class of boundary value problems
We consider the $n$'th order ordinary differential equation $(-1)^{n-k} y^{(n)}=\lambda a(t) f(y)$, $t\in[0,1]$, $n\geq 3$ together with the boundary condition $y^{(i)}(0)=0$, $0\leq i\leq k-1$ and $y^{(l)}=0$, $j\leq l\leq j+n-k-1$, for $1\leq j\leq k-1$ fixed. Values of $\lambda$ are characterized so that the boundary value problem has a positive solution.
 1 13 25 . .
1999-01-01 0000-00-00 58 yes 57 no 25 1 1999 13 0 Asymptotic stability in differential equations with unbounded delay
In this paper we consider a functional differential equation of the form
$$x'=F(t,x,\int_0^t C(at-s) x(s)\,ds)$$
where $a$ is a constant satisfying $0<a<\infty$. Thus, the integral represents the memory of past positions of the solution $x$. We make the assumption that $\int_0^\infty |C(t)|\, dt<\infty$ so that this is a fading memory problem and we are interested in studying the effects of that memory over all those values of $a$. Very different properties of solutions emerge as we vary $a$ and we are interested in developing an approach which handles them in a unified way.
 1 19 3 . .
See also an addendum to this paper: EJQTDE, No. 3. (2001)
 1999-01-01 0000-00-00 857 yes 66 no 58 1 2000 1 0 Oscillation theorems for nonlinear differential equations
We establish new oscillation theorems for the nonlinear differential equation
$$[a(t)\psi(x(t))|x'(t)|^{\alpha-1}x'(t)]'+q(t)f(x(t))=0, \alpha>0$$
where $a,q:[t0,\infty)\rightarrow R, \psi,f:R\rightarrow R$ are continuous, $a(t)>0$ and $\psi(x)>0$, $xf(x)>0$ for $x\not=0$. These criteria involve the use of averaging functions.
 1 21 866 . .
2000-01-01 0000-00-00 1763 yes 64 1 2000 2 0 Nonlinear eigenvalue problems for higher order Lidstone boundary value problems
In this paper, we consider the Lidstone boundary value problem $y^{(2m)}(t) = \lambda a(t)f(y(t), ..., y^{(2j)}(t), ... y^{(2(m-1))}(t), 0 < t < 1, y^{(2i)}(0) = 0 = y^{(2i)}(1), i = 0, ..., m - 1$, where $(-1)^m f > 0$ and $a$ is nonnegative. Growth conditions are imposed on $f$ and inequalities involving an associated Green's function are employed which enable us to apply a well-known cone theoretic fixed point theorem. This in turn yields a $\lambda$ interval on which there exists a nontrivial solution in a cone for each $\lambda$ in that interval. The methods of the paper are known. The emphasis here is that $f$ depends upon higher order derivatives. Applications are made to problems that exhibit superlinear or sublinear type growth.
 1 8 25 . .
2000-01-01 0000-00-00 107 yes 20 1 2000 3 0 Self--similar solutions of convection--diffusion processes
Geometric properties of self--similar solutions to the equation $ u_t = u_{xx} + \gamma(u^q)_x,\ x > 0,\ t > 0 $ are studied, $ q $ is positive and $ \gamma\in \mathbb{R}\setminus\{0\}$. Two critical values of $ q $ (namely 1 and 2) appear the corresponding shapes are of very different nature.
 1 18 7 . .
2000-01-01 0000-00-00 59 yes 59 1 2000 4 0 A necessary and sufficient condition for the oscillation in a class of even order neutral differential equations
The even order neutral differential equation
$$\frac{d^n}{dt^n} [ x(t) + \lambda x(t-\tau) ] + f(t,x(g(t))) = 0\leqno{(1.1)}$$
is considered under the following conditions: $n\ge 2$ is even; $\lambda>0$; $\tau>0$; $g \in C[t_0,\infty)$, $\lim_{t\to\infty} g(t) = \infty$; $f \in C([t_0,\infty) \times {\bf R})$, $u f(t,u) \ge 0$ for $(t,u) \in [t_0,\infty) \times {\bf R}$, and $f(t,u)$ is nondecreasing in $u \in {\bf R}$ for each fixed $t\ge t_0$. It is shown that equation (1.1) is oscillatory if and only if the non-neutral differential equation
$$x^{(n)}(t) + \frac{1}{1+\lambda} f(t,x(g(t))) = 0$$
is oscillatory.
 1 27 857 . .
2000-01-01 0000-00-00 1576 yes 62 1 2000 5 0 Periodic solutions of the neutral Duffing Equations
We consider the neutral delay Duffing Equations of the form
$$ax''(t)+bx'(t)+cx(t)+g(x(t-\tau_1), \ x'(t-\tau_2), x''(t-\tau_3))=p(t)=p(t+2\pi).$$
and establish a sufficient coudition for the existence of $2\pi$-periodic solution of above equations.
 1 14 1455 . .
2000-01-01 0000-00-00 29 yes 104 no 105 no 66 1 2000 6 0 Asymptotic behaviour of positive solutions of the model which describes cell differentiation
In this paper we will study the asymptotic behaviour of positive solutions to the system
$$\left|
\begin{array}{lcr}
x_1^{\prime}(t)={{A(t)}\over {1+x_2^n(t)}}-x_1(t)\\
x_2^{\prime}(t)={{B(t)}\over {1+x_1^n(t)}}-x_2(t),
\end{array}
\right.\leqno{(1)}$$
where $A$ and $B$ belong to ${\cal C}_+$ and ${\cal C}_+$ is the set of continuous functions $g:{\cal R}\longrightarrow {\cal R}$, which are bounded above and below by positive constants. $n$ is fixed natural number. The system (1) describes cell differentiation, more precisely - its passes from one regime of work to other without loss of genetic information. The variables $x_1$ and $x_2$ make sense of concentration of specific metabolits. The parameters $A$ and $B$ reflect degree of development of base metabolism. The parameter $n$ reflects the highest row of the repression's reactions.
 1 17 25 . .
2000-01-01 0000-00-00 110 yes 77 1 2000 7 0 Fucik spectra for vector equations
Let $L:\hbox{dom} L\subset L^2(\Omega;R^N)\rightarrow L^2(\Omega;R^N)$ be a linear operator, $\Omega$ being open and bounded in $R^M$. The aim of this paper is to study the Fu\v c\'\i k spectrum for vector problems of the form $Lu=\alpha Au^+ -\beta Au^-$, where $A$ is an $N\times N$ matrix, $\alpha, \beta$ are real numbers, $u^+$ a vector defined componentwise by $(u^+)_i=\max\{u_i,0\}$, $u^-$ being defined similarly. With $\lambda^*$ an eigenvalue for the problem $Lu=\lambda Au$, we describe (locally) curves in the Fu\v c\'\i k spectrum passing through the point $(\lambda^*,\lambda^*)$, distinguishing different cases illustrated by examples, for which Fu\v c\'\i k curves have been computed numerically.
 1 24 16 . .
2000-01-01 0000-00-00 125 yes 70 1 2000 8 0 Floquet Theory for Linear Differential Equations with Meromorphic Solutions
If $A$ is a $\omega$-periodic matrix Floquet's theorem states that the differential equation $y'=A y$ has a fundamental matrix $P(x)\exp(J x)$ where $J$ is constant and $P$ is $\omega$-periodic, i.e., $P(x)=P^*(\e^{2\pi ix/\omega})$. We prove here that $P^*$ is rational if $A$ is bounded at the ends of the period strip and if all solutions of $y'=A y$ are meromorphic. This version of Floquet's theorem is important in the study of certain integrable systems.
 1 6 8 . .
2000-01-01 0000-00-00 117 yes 27 1 2000 9 0 Hybrid dynamical systems vs. ordinary differential equations: Examples of a "pathological" behavior
We investigate the controlled harmonic oscillator
\begin{equation}\label{eq3.1}
\ddot{\xi}+\xi=u,
\end{equation}
where an external force (the control function) $u$ depends on the coordinate $\xi$, only. It can be shown that no ordinary (even nonlinear) feedback controls of the form $u=f(\xi(t))$ can asymptotically stabilize the solutions of the system (\ref{eq3.1}). However, one is able to make the system (\ref{eq3.1}) asymptotically stable if one designs a special feedback control $u$ depending on $\xi(\cdot)$ which is called {\it a hybrid feedback control}. We demonstrate in the paper that the dynamics of a typical linear system of ordinary differential equations equipped with a linear hybrid feedback control possesses some irregular properties that dynamical systems without delay do not have. For example, solutions with different initial conditions may cross or even partly coincide. This proves that the hybrid dynamics cannot, in general, be described by a system of ordinary differential equations, neither linear, nor nonlinear, so that time-delays have to be incorporated into the system.
 1 10 4 . .
2000-01-01 0000-00-00 14 yes 68 no 69 no 79 1 2000 10 0 The uniqueness of the periodic solution for a class of differential equations
In this paper we are concerned with a class of nonlinear differential equations and obtaining the sufficient conditions for the uniqueness of the periodic solution by using Brouwer's fixed point theory and the Sturm Theorem.
 1 9 1455 . .
2000-01-01 0000-00-00 128 yes 78 1 2001 1 0 Existence results for first order impulsive semilinear evolution inclusions
In this paper the concepts of lower mild and upper mild solutions combined with a fixed point theorem for condensing maps and the semigroup theory are used to investigate the existence of mild solutions for first order impulsive semilinear evolution inclusions.
 1 12 3 . .
2001-01-01 0000-00-00 57 yes 71 no 70 no 83 1 2001 2 0 Radial symmetric solutions of the Cahn-Hilliard equation with degenerate mobility
In this paper we study the radial symmetric solutions of the two-dimensional Cahn-Hilliard equation with degenerate mobility. We adopt the method of parabolic regularization. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence and the nonnegativity of weak solutions. Keywords. Cahn-Hilliard equation, radial solution, degenerate mobility, nonnegativity.
 1 14 25 . .
2001-01-01 0000-00-00 134 yes 135 no 91 1 2001 3 0 Addendum to asymptotic stability in differential equations with unbounded delay
This addendum concerns the paper of the above title found in EJQTDE No. 13 (1999). Throughout that paper was the tacit assumption that the coefficient functions $h(t)$, $b(t)$, and $C(t)$ are all continuous on their respective domains. Every result, as well as the existence result stated at the end of the first section, depended on those functions being continuous. A search of the paper indicates that we failed to state this. We regret any inconvenience which this may have caused any reader.
 1 1 3 . . 2001-01-01 0000-00-00 857 yes 66 no 80 1 2001 4 0 Exact multiplicity of positive solutions in semipositone problems with concave-convex type nonlinearities
We study the existence, multiplicity, and stability of positive solutions to:
$$\eqalign{- u''(x) &= \lambda f(u(x)) \ \text{for} \ x \in (-1, 1), \lambda > 0, \cr
u(-1)&= 0\ = u(1) ,}$$
where $f : [0, \infty) \to \Bbb R$ is semipositone ($f(0)<0$) and superlinear ($\lim_{t \to \infty} f(t) /t = \infty)$. We consider the case when the nonlinearity $f$ is of concave-convex type having exactly one inflection point. We establish that $f$ should be appropriately concave (by establishing conditions on $f$) to allow multiple positive solutions. For any $\lambda > 0$, we obtain the exact number of positive solutions as a function of $f(t)/t$ and establish how the positive solution curves to the above problem change. Also, we give examples where our results apply. This work extends the work in [1] by giving a complete classification of positive solutions for concave-convex type nonlinearities.
 1 9 3 . .
2001-01-01 0000-00-00 130 yes 129 no 97 1 2001 5 0 Existence and attractors of solutions for nonlinear parabolic systems
We prove existence and asymptotic behaviour results for weak solutions of a mixed problem (S). We also obtain the existence of the global attractor and the regularity for this attractor in $\left[H^{2}(\Omega )\right] ^{2}$ and we derive estimates of its Haussdorf and fractal dimensions.
 1 16 3 . .
2001-01-01 0000-00-00 149 yes 148 no 85 1 2001 6 0 Algebraic structure of space and field
We investigate an algebraic structure of the space of solutions of autonomous nonlinear differential equations of certain type. It is shown that for these equations infinitely many binary algebraic laws of addition of solutions exist. We extract commutative and conjugate commutative groups which lead to the conjugate differential equations. Besides one is being able to write down particular form of extended Fourier series for these equations. It is shown that in space with a moving field, there always exist metrics geodesics of which are the solutions of a given differential equation and its conjugate equation. Connection between the invariant group and algebraic structure of solution space has also been studied.
 1 52 11 . .
2001-01-01 0000-00-00 138 yes 137 no 93 1 2001 7 0 Uniform boundedness and global existence of solutions for reaction-diffusion systems with a balance law and a full matrix of diffusion coefficients
The purpose of this paper is to prove uniform boundedness and so global existence of solutions for reaction-diffusion systems with a full matrix of diffusion coefficients satisfying a balance law. Our technics are based on invariant regions and Lyapunov functional methods. The nonlinearity of the reaction term which we take positive in an invariant region has been supposed to be polynomial.
 1 9 5 . .
2001-01-01 0000-00-00 143 yes 103 1 2001 8 0 An existence theorem for parabolic equations on $R^N$ with discontinuous nonlinearity
We prove existence of solutions for parabolic initial value problems $\partial_t u = \Delta u + f(u)$ on $R^N$ , where $f : R \rightarrow R$ is a bounded, but possibly discontinuous function.
 1 9 3 . .
2001-01-01 0000-00-00 157 yes 158 no 88 1 2002 1 0 The asymptotic nature of a class of second order nonlinear system
In this paper, we obtain some results on the nonoscillatory behaviour of the system (1), which contains as particular cases, some well known systems. By negation, oscillation criteria are derived for these systems. In the last section we present some examples and remarks, and various well known oscillation criteria are obtained.
 1 22 857 . .
2002-01-01 0000-00-00 1963 yes 111 1 2002 2 0 Global existence of solutions for reaction-diffusion systems with a full matrix of diffusion coefficients and nonhomogeneous boundary conditions
In this article, we generalize the results obtained in [16] concerning uniform bounds and so global existence of solutions for reaction-diffusion systems with a full matrix of diffusion coefficients satisfying a balance law and with homogeneous Neumann boundary conditions. Our techniques are based on invariant regions and Lyapunov functional methods. We demonstrate that our results remain valid for nonhomogeneous boundary conditions and with out balance law's condition. The nonlinear reaction term has been supposed to be of polynomial growth.
 1 10 5 . .
2002-01-01 0000-00-00 143 yes 116 1 2002 3 0 Limits of solutions of a perturbed linear differential equation
Using interesting techniques, an existence result for the problem $\ddot{x}+2f\left( t\right) \dot{x}+x+g\left( t,x\right) =0,$ $\lim\limits_{t\rightarrow +\infty }x\left( t\right) =\lim\limits_{t\rightarrow +\infty }\dot{x}\left( t\right) =0,$ is given in [2]. This note treates the same problem via Schauder-Tychonoff and Banach theorems.
 1 11 857 . .
2002-01-01 0000-00-00 170 yes 171 no 100 1 2002 4 0 Periodic perturbations of non-conservative second order differential equations
Consider the Lienard system $u''+f(u) u'+g(u)=0$ with an isolated periodic solution. This paper concerns the behavior of periodic solutions of Lienard system under small periodic perturbations.
 1 12 5 . .
2002-01-01 0000-00-00 152 yes 98 1 2002 5 0 Estimation of the hyper-order of entire solutions of complex linear ordinary differential equations whose coefficients are entire functions
We investigate the growth of solutions of the differential equation $f^{\left( n\right) }+A_{n-1}\left( z\right) f^{\left( n-1\right) }+...+A_{1}\left( z\right) f^{^{\prime }}+A_{0}\left( z\right) f=0,$ where $A_{0}\left( z\right) ,...,A_{n-1}\left( z\right) $\ \ are\ entire functions with $A_{0}\left( z\right) \not\equiv 0$. We estimate the hyper-order with respect to the conditions of $A_{0}\left( z\right) ,...,A_{n-1}\left( z\right) $\ if\ $f\not\equiv 0$ has infinite order.
 1 8 3 . .
2002-01-01 0000-00-00 1377 yes 119 1 2002 6 0 On a fixed point theorem Krasnoselskii-Shafer type
In this paper a variant of a fixed point theorem to Krasnoselskii-Schaefer type is proved and it is further applied to certain nonlinear integral equation of mixed type for proving the existence of the solution.
 1 9 857 . .
2002-01-01 0000-00-00 2747 yes 108 1 2002 7 0 Decay rates for solutions of semilinear wave equations with a memory condition at the boundary
In this paper, we study the stability of solutions for semilinear wave equations whoseboundary condition includes a integral that represents the memory effect. We show that the dissipation is strong enough to produce exponential decay of the solution, provided the relaxation function also decays exponentially. When the relaxation function decays polinomially, we show that the solution decays polynomially and with the same rate.
 1 17 25 . .
2002-01-01 0000-00-00 132 yes 118 1 2002 8 0 Blowup estimates for a mutualistic model in ecology
The cooperating two-species Lotka-Volterra model is discussed. We study the blowup properties of solutions to a parabolic system with homogeneous Dirichlet boundary conditions. The upper and lower bounds of blowup rate are obtained.
 1 14 3 . .
2002-01-01 0000-00-00 141 yes 123 1 2002 9 0 Evanescent solutions for linear ordinary differential equations
The problem of existence of the solutions for ordinary differential equations vanishing at $\pm \infty $ is considered.
 1 12 857 . .
2002-01-01 0000-00-00 170 yes 113 1 2002 10 0 Method of the quasilinearization for nonlinear impulsive differential equations with linear boundary conditions
The method of quasilinearization for nonlinear impulsive differential equations with linear boundary conditions is studied. The boundary conditions include periodic boundary conditions. It is proved the convergence is quadratic.
 1 14 3 . .
2002-01-01 0000-00-00 107 yes 168 no 107 1 2002 11 0 Elastic membrane equation in bounded and unbounded domains
The small-amplitude motion of a thin elastic membrane is investigated in $n$-dimensional bounded and unbounded domains, with $n\in N$. Existence and uniqueness of solutions are established. Asymptotic of solutions is proved too.
 1 21 3 . .
2002-01-01 0000-00-00 163 yes 96 1 2002 12 0 Some stability and boundedness criteria for a class of Volterra integro-differential systems
Using Lyapunov and Lyapunov-like functionals, we study the stability and boundedness of the solutions of a system of Volterra integrodifferential equations. Our results, also extending some of the more well-known criteria, give new sufficient conditions for stability of the zero solution of the nonperturbed system, and prove that the same conditions for the perturbed system yield boundedness when the perturbation is $L^2$.
 1 20 857 . .
2002-01-01 0000-00-00 150 yes 133 1 2002 13 0 Nonresonance impulsive higher order functional nonconvex-valued differential inclusions
In this paper, the authors investigate the existence of solutions for nonresonance impulsive higher order functional differential inclusions in Banach spaces with nonconvex valued right hand side. They present two results. In the first one, they rely on a fixed point theorem for contraction multivalued maps due to Covitz and Nadler, and for the second one, they use Schaefer's fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values.
 1 13 5 . .
2002-01-01 0000-00-00 71 yes 7 no 57 no 70 no 90 1 2002 14 0 Continuity, compactness, fixed points, and integral equations
An integral equation, $x(t)=a(t)-\int^t_{-\infty} D(t,s)g(x(s))ds$ with $a(t)$ bounded, is studied by means of a Liapunov functional. There results an {\it{a}} {\it{priori}} bound on solutions. This gives rise to an interplay between continuity and compactness and leads us to a fixed point theorem of Schaefer type. It is a very flexible fixed point theorem which enables us to show that the solution inherits properties of $a(t)$, including periodic or almost periodic solutions in a Banach space.
 1 13 858 . .
2002-01-01 0000-00-00 857 yes 3 no 121 1 2002 15 0 Positive solutions of three-point nonlinear second order boundary value problem
In this paper we apply a cone theoretic fixed point theorem and obtain conditions for the existence of positive solutions to the three-point nonlinear second order boundary value problem
$$ u''(t)+\lambda a(t)f(u(t)) = 0, \;\;\;t\in(0,1)$$
$$u(0)=0,\;\;\;\; \alpha u(\eta)=u(1),$$
where $0<\eta<1$ and $0<\alpha <\frac{1}{\eta}.$
 1 11 3 . .
2002-01-01 0000-00-00 113 yes 136 1 2002 16 0 On nonnegative radial entire solutions of second order quasilinear elliptic systems
In this article we consider the second order quasilinear elliptic system of the form
$$\Delta_{p_i} u_i=H_i(|x|)u_{i+1}^{\alpha_i}, x\in R^N, i=1,2,...,m$$
with nonnegative continuous function $H_i$. Sufficient conditions are given to have nonnegative nontrivial radial entire solutions. When $H_i$, $i = 1, 2, ..., m$, behave like constant multiples of $|x|^\lambda$, $\lambda\in R$, we can completely characterize the existence property of nonnegative nontrivial radial entire solutions.
 1 34 6 . .
2002-01-01 0000-00-00 198 yes 143 1 2002 17 0 Spectrum of one dimensional p-Laplacian operator with indefinite weight
This paper is concerned with the nonlinear boundary eigenvalue problem
$$-(|u'|^{p-2}u')'=\lambda m|u|^{p-2}u\qquad u \in I=]a,b[,\quad u(a)=u(b)=0,$$
where $p>1$, $\lambda$ is a real parameter, $m$ is an indefinite weight, and $a$, $b$ are real numbers. We prove there exists a unique sequence of eigenvalues for this problem. Each eigenvalue is simple and verifies the strict monotonicity property with respect to the weight $m$ and the domain $I$, the k-th eigenfunction, corresponding to the $k$-th eigenvalue, has exactly $k-1$ zeros in $(a,b)$. At the end, we give a simple variational formulation of eigenvalues.
 1 11 3 . .
2002-01-01 0000-00-00 156 yes 154 no 2112 no 137 1 2002 18 0 On the existence and smoothness of radially symmetric solutions of a BVP for a class of nonlinear, non-Lipschitz perturbations of the Laplace equation
The existence of radially symmetric solutions $u(x;a)$ to the Dirichlet problems
$$\Delta u(x)+f(|x|,u(x),|\nabla u(x)|)=0\qquad x\in B,\ u|_\Gamma=a\in{\R}\ (\Gamma:=\partial B)$$
is proved, where $B$ is the unit ball in ${\R}^n$ centered at the origin $(n\ge2)$, $a$ is arbitrary $(a>a_0\ge-\infty);f$ is positive, continuous and bounded. It is shown that these solutions belong to $C^2(\ov{B})$. Moreover, in the case $f\in C^1$ a sufficient condition (near necessary) for the smoothness property $u(x;a)\in C^3(\ov{B})\quad\forall a>a_0$ is also obtained.
 1 28 3 . .
2002-01-01 0000-00-00 122 yes 147 1 2003 1 0 Stability of simple periodic solutions of neutral functional differential equations
We study the stability property of a simple periodic solution of an autonomous neutral functional differential equation (NFDE) of the form
$${d\over dt} D(x_t) = f (x_t).$$
A new proof based on local integral manifold theory and the implicit function theorem is given for the classical result that a simple periodic orbit of the equation above is asymptotically orbitally stable with asymptotic phase. The technique used overcomes the difficulty that the solution operator of a NFDE does not smooth as $t$ increases.
 1 11 3 . .
2003-01-01 0000-00-00 206 yes 207 no 138 1 2003 2 0 Alternative analysis generated by a differential equation
It was shown in [1] that for a wide class of differential equations there exist infinitely many binary laws of addition of solutions such that every binary law has its conjugate. From this set of operations we extract commutative algebraic object that is a pair of two alternative to each other fields with common identity elements.
The goal of the present paper is to detect those mathematical constructions that are related to the existence of alternative fields dictated by differential equations. With this in mind we investigate differential and integral calculus based on the commutative algebra that is generated by a given differential equation. It turns out that along with the standard differential and integral calculus there always exists an isomorphic alternative calculus. Moreover, every system of differential equations generates its own calculus that is isomorphic (or homomorphic) to the standard one. The given system written in its own calculus appears to be linear.
It is also shown that there always exist two alternative to each other geometries, and matrix algebra has its alternative isomorphic to the classical one.
 1 31 3 . .
See also an addendum to this paper: EJQTDE, No. 7. (2004)
 2003-01-01 0000-00-00 138 yes 137 no 117 1 2003 3 0 Initial boundary value problems for second order impulsive functional differential inclusions
In this paper we investigate the existence of solutions for initial and boundary value problems for second order impulsive functional differential inclusions. We shall rely on a fixed point theorem for contraction multivalued maps due to Covitz and Nadler.
 1 10 13 . .
2003-01-01 0000-00-00 71 yes 172 no 145 1 2003 4 0 Global existence of solutions in invariant regions for reaction-diffusion systems with a balance law and a full matrix of diffusion coefficients
In this paper we generalize a result obtained in [15] concerning uniform boundedness and so global existence of solutions for reaction-diffusion systems with a general full matrix of diffusion coefficients satisfying a balance law. Our techniques are based on invariant regions and Lyapunov functional methods. The nonlinearity of the reaction term which we take positive in an invariant region has been supposed to be polynomial or of weak exponential growth.
 1 10 5 . .
2003-01-01 0000-00-00 143 yes 149 1 2003 5 0 Some remarks on a fixed point theorem of Krasnoselskii
Using a particular locally convex space and Schaefer's theorem, a generalization of Krasnoselskii's fixed point Theorem is proved. This result is further applied to certain nonlinear integral equation proving the existence of a solution on $\R_{+}=[0,+\infty).$
 1 15 857 . .
2003-01-01 0000-00-00 170 yes 142 1 2003 6 0 Non-existence criteria for Laurent polynomial first integrals
In this paper we derived some simple criteria for non-existence and partial non-existence Laurent polynomial first integrals for a general nonlinear systems of ordinary differential equations $\dot x = f(x)$, $x \in R^n$ with $f(0) = 0$. We show that if the eigenvalues of the Jacobi matrix of the vector field $f(x)$ are $Z$-independent, then the system has no nontrivial Laurent polynomial integrals.
 1 11 25 . .
2003-01-01 0000-00-00 2032 yes 204 no 129 1 2003 7 0 Coexistence for a resource-based growth model with two resources
We investigate the coexistence of positive steady-state solutions to a parabolic system, which models a single species on two growth-limiting, non-reproducing resources in an un-stirred chemostat with diffusion. We establish the existence of a positive steady-state solution for a range of the parameter $(m,n)$, the bifurcation solutions and the stability of bifurcation solutions. The proof depends on the maximum principle, bifurcation theorem and perturbation theorem.
 1 11 25 . .
2003-01-01 0000-00-00 189 yes 190 no 156 1 2003 8 0 A system of abstract measure delay differential equations
In this paper existence and uniqueness results for an abstract measure delay differential equation are proved, by using Leray-Schauder nonlinear alternative, under Carathéodory conditions.
 1 14 857 . .
2003-01-01 0000-00-00 2747 yes 215 no 70 no 141 1 2003 9 0 Complete description of the set of solutions to a strongly nonlinear O.D.E's
We give a complete description of the set of solutions to the boundary value problem
\[
\left\{
\begin{array}{c}
-\left( \varphi \left( u^{\prime }\right) \right) ^{\prime }=f\left(
u\right) \text{ in }\left( 0,1\right) \\
u\left( 0\right) =u\left( 1\right) =0
\end{array}
\right.
\]
where $\varphi $ is an odd increasing homeomorphism of $\Bbb{R}$ concave on $\Bbb{R}^{+}$ and $f$ $\in C\left( \Bbb{R}\text{, }\Bbb{R}\right) $is odd and superlinear.
 1 18 857 . .
2003-06-12 0000-00-00 1594 yes 150 1 2003 10 0 Cahn-Hilliard Equation with Terms of Lower Order and non-constant Mobility
In this paper, we study the global existence of classical solutions for the Cahn-Hilliard equation with terms of lower order and non-constant mobility. Based on the Schauder type estimates, under some assumptions on the mobility and terms of lower order, we establish the global existence of classical solutions.
 1 9 3 . .
2003-06-12 0000-00-00 135 yes 124 1 2003 11 0 Existence results for impulsive semilinear damped differential inclusions
In this paper we investigate the existence of mild solutions for first and second order impulsive semilinear evolution inclusions in separable Banach spaces. By using suitable fixed point theorems, we study the case when the multivalued map has convex and nonconvex values.
 1 19 3 . .
2003-06-12 0000-00-00 71 yes 57 no 70 no 172 no 134 1 2003 12 0 Nonnegative solutions of parabolic operators with low-order terms
We develop the harmonic analysis approach for parabolic operator with one order term in the parabolic Kato class on $C^{1,1}$-cylindrical domain $\Omega$. We study the boundary behaviour of nonnegative solutions. Using these results, we prove the integral representation theorem and the existence of nontangential limits on the boundary of $\Omega$ for nonnegative solutions. These results extend some first ones proved for less general parabolic operators.
 1 16 23 . .
2003-06-24 0000-00-00 196 yes 159 1 2003 13 0 Asymptotic behavior of solutions of nonlinear differential equations and generalized guiding functions
Let $f:\R\times \R^{N}\rightarrow \R^{N}$ be a continuous function and let $h:\R\rightarrow \R$ be a continuous and strictly positive function. A sufficient condition such that the equation $\dot{x}=f\left( t,x\right) $ admits solutions $x:\R\rightarrow \R^{N}$ satisfying the inequality $\left| x\left( t\right) \right| \leq k\cdot h\left( t\right) ,$ $t\in \R,$ $k>0$, where $\left| \cdot \right| $ is the euclidean norm in $\R^{N},$ is given. The proof of this result is based on the use of a special function of Lyapunov type, which is often called guiding function. In the particular case $h\equiv 1$, one obtains known results regarding the existence of bounded solutions.
 1 9 857 . .
2003-07-07 0000-00-00 170 yes 146 1 2003 14 0 A functional integral inclusion involving Carathéodories
In this paper the existence of extremal solutions of a functional integral inclusion involving Carathéodory is proved under certain monotonicity conditions. Applications are given to some initial and boundary value problems of ordinary differential inclusion for proving the existence of extremal solutions. Our results generalize the results of Dhage [8] under weaker conditions and complement the results of O'Regan [16].
 1 18 3 . .
2003-09-08 0000-00-00 2747 yes 158 1 2003 15 0 On the structure of spectra of travelling waves
The linear stability of the travelling wave solutions of a general reaction-diffusion system is investigated. The spectrum of the corresponding second order differential operator $L$ is studied. The problem is reduced to an asymptotically autonomous first order linear system. The relation between the spectrum of $L$ and the corresponding first order system is dealt with in detail. The first order system is investigated using exponential dichotomies. A self-contained short presentation is shown for the study of the spectrum, with elementary proofs. An algorithm is given for the determination of the exact position of the essential spectrum. The Evans function method for determining the isolated eigenvalues of $L$ is also presented. The theory is illustrated by three examples: a single travelling wave equation, a three variable combustion model and the generalized KdV equation.
 1 19 5 . .
2003-10-18 0000-00-00 157 yes 163 1 2003 16 0 Remarks on null controllability for semilinear heat equation in moving domains
We investigate in this article the null conrollability for the semilinear heat operator $u' - \Delta u +f(u)$ in a domain which boundary is moving with the time $t$.
 1 32 13 . .
2003-10-22 0000-00-00 218 yes 219 no 220 no 148 1 2003 17 0 Uniqueness of bounded solutions to a viscous diffusion equation
In this paper we prove the uniqueness of bounded solutions to a viscous diffusion equation based on approximate Holmgren's approach.
 1 8 3 . .
2003-10-22 0000-00-00 1569 yes 134 no 166 1 2003 18 0 On the uniformly continuity of the solution map for two dimensional wave maps
The aim of this paper is to analyse the properties of the solution map to the Cauchy problem for the wave map equation with a source term, when the target is the hyperboloid ${\cal H}^2$ that is embedded in ${\cal R}^3$. The initial data are in ${\dot H}^1\times L^2$. We prove that the solution map is not uniformly continuous.
1 7 13 . .
2003-10-10 0000-00-00 110 yes 222 no 167 1 2003 19 0 The generalized method of quasilinearization and nonlinear boundary value problems with integral boundary conditions
The generalized method of quasilinearization is applied to obtain a monotone sequence of iterates converging uniformly and rapidly to a solution of second order nonlinear boundary value problem with nonlinear integral boundary conditions.
 1 15 107 . .
2003-10-22 0000-00-00 221 yes 120 1 2003 20 0 Perturbed integral equations in modular function spaces
We focus our attention on a class of perturbed integral equations in modular spaces, by using fixed point Theorem I.1 (see [1]).
 1 7 3 . .
2003-11-10 0000-00-00 174 yes 175 no 128 1 2003 21 0 Bifurcation of nonlinear elliptic system from the first eigenvalue
We study the following bifurcation problem in a bounded domain $\Omega$ in $\RR^N$:
$$\left\{\begin{array}{lll}
-\Delta_p u=&\lambda |u|^{\alpha}|v|^{\beta}v \,+ f(x,u,v,\lambda)&
\mbox{in} \ \Omega\\
-\Delta_q v=&\lambda |u|^{\alpha}|v|^{\beta}u \, + g(x,u,v,\lambda) &
\mbox{in} \ \Omega\\
(u,v)\in & W_0^{1,p}(\Omega)\times W_0^{1,q}(\Omega). & \
\end{array}
\right.
$$
We prove that the principal eigenvalue $\lambda_1$ of the following eigenvalue problem
$$\left\{\begin{array}{lll}
-\Delta_p u=&\lambda |u|^{\alpha}|v|^{\beta}v \,& \mbox{in} \ \Omega\\
-\Delta_q v=&\lambda |u|^{\alpha}|v|^{\beta}u \,& \mbox{in} \ \Omega\\
(u,v)\in & W_0^{1,p}(\Omega)\times W_0^{1,q}(\Omega)& \
\end{array}
\right.$$
is simple and isolated and we prove that $(\lambda_1,0,0)$ is a bifurcation point of the system mentioned above.
 1 18 3 . .
2003-10-29 0000-00-00 186 yes 187 no 188 no 174 1 2003 22 0 Symmetric solutions to minimization of a p-energy functional with ellipsoid value
The author proves the $W^{1,p}$ convergence of the symmetric minimizers
$u_{\varepsilon}=(u_{\varepsilon 1},u_{\varepsilon 2},u_{\varepsilon 3})$ of a p-energy functional as $\varepsilon \to 0$, and the zeros of $u_{\varepsilon 1}^2+u_{\varepsilon 2}^2$ are located roughly. In addition,the estimates of the convergent rate of $u_{\varepsilon 3}^2$ (to $0$) are presented. At last, based on researching the Euler-Lagrange equation of symmetric solutions and establishing its $C^{1,\alpha}$ estimate, the author obtains the $C^{1,\alpha}$ convergence of some symmetric minimizer.
 1 21 3 . .
2003-12-23 0000-00-00 212 yes 175 1 2004 1 0 Existence theory for nonlinear functional boundary value problems
In this paper the existence of a solution of a general nonlinear functional two point boundary value problem is proved under mixed generalized Lipschitz and Carath\'eodory conditions. An existence theorem for extremal solutions is also proved under certain monotonicity and weaker continuity conditions. Examples are provided to illustrate the theory developed in this paper.
 1 15 107 . .
2004-01-06 0000-00-00 2747 yes 57 no 176 1 2004 2 0 Eigenvalue problems for a three-point boundary-value problem on a time scale
Let $\mathbb{T}$ be a time scale such that $0, T \in \mathbb{T}$. We us a cone theoretic fixed point theorem to obtain intervals for $\lambda$ for which the second order dynamic equation on a time scale,
\begin{gather*}
u^{\Delta\nabla}(t) + \lambda a(t)f(u(t)) = 0, \quad t \in (0,T) \cap \mathbb{T},\\
u(0) = 0, \quad \alpha u(\eta) = u(T),
\end{gather*}
where $\eta \in (0, \rho(T)) \cap \mathbb{T}$, and $0 < \alpha <T/\eta$, has a positive solution.
 1 10 857 . .
2004-01-12 0000-00-00 230 yes 113 no 177 1 2004 3 0 Fixed points for some non-obviously contractive operators defined in a space of continuous functions
Let $X$ be an arbitrary (real or complex) Banach space, endowed with the norm $\left| \cdot \right| .$ Consider the space of the continuous functions $C\left( \left[ 0,T\right] ,X\right) $ $\left( T>0\right) $, endowed with the usual topology, and let $M$ be a closed subset of it. One proves that each operator $A:M\rightarrow M$ fulfilling for all $x,y\in M$ and for all $t\in \left[ 0,T\right] $ the condition
\begin{eqnarray*}
\left| \left( Ax\right) \left( t\right) -\left( Ay\right) \left( t\right)
\right| &\leq &\beta \left| x\left( \nu \left( t\right) \right) -y\left( \nu
\left( t\right) \right) \right| + \\
&&+\frac{k}{t^{\alpha }}\int_{0}^{t}\left| x\left( \sigma \left( s\right)
\right) -y\left( \sigma \left( s\right) \right) \right| ds,
\end{eqnarray*}
(where $\alpha ,$ $\beta \in \lbrack 0,1)$, $k\geq 0$, and $\nu ,$ $\sigma :\left[ 0,T\right] \rightarrow \left[ 0,T\right] $ are continuous functions such that $\nu \left( t\right) \leq t,$ $\sigma \left( t\right)\leq t,$ $\forall t\in \left[ 0,T\right] $) has exactly one fixed point in $M $. Then the result is extended in $C\left( \R_{+},X\right) ,$ where $\R_{+}:=[0,\infty ).$
 1 7 857 . .
2004-02-01 0000-00-00 170 yes 171 no 178 1 2004 4 0 Representations of mild solutions of time-varying linear stochastic equations and the exponential stability of periodic systems
The main object of this paper is to give a representation of the covariance operator associated to the mild solutions of time-varying,linear, stochastic equations in Hilbert spaces. We use this representation to obtain a characterization of the uniform exponential stability of linear stochastic equations with periodic coefficients.
 1 22 4 . .
2004-02-02 0000-00-00 231 yes 160 1 2004 5 0 Complete polynomial vector fields in simplexes with application to evolutionary dynamics
We describe the complete polynomial vector fields and their fixed points in a finite-dimensional simplex and we apply the results to differential equations of genetical evolution models.
 1 10 858 . .
2004-02-10 0000-00-00 217 yes 182 1 2004 6 0 New criteria for the existence of periodic and almost periodic solutions for some evolution equations in Banach spaces
In this work we give a new criteria for the existence of periodic and almost periodic solutions for some differential equation in a Banach space. The linear part is nondensely defined and satisfies the Hille-Yosida condition. We prove the existence of periodic and almost periodic solutions with condition that is more general than the known exponential dichotomy. We apply the new criteria for the existence of periodic and almost periodic solutions for some partial functional differential equation whose linear part is nondensely defined.
 1 12 867 . .
2004-02-18 0000-00-00 234 yes 235 no 183 1 2004 7 0 Addendum to alternative analysis generated by a differential equation
This addendum concerns the paper of the above title found in EJQTDE No. 2 (2003 ). On page 3, before (2.2), instead of "Applying the mean value theorem" it should read "By simple calculations". It does not change any results presented in the paper, but excludes the mistake of applying the mean value theorem for a complex valued function of a real variable. The mean value theorem is not needed.
 1 1 3 . . 2004-03-07 0000-00-00 138 yes 137 no 185 1 2004 8 0 Positive solutions for first order nonlinear functional boundary value problems on infinite intervals
In this paper we study a boundary value problem for a first order functional differential equation on an infinite interval. Using fixed point theorems on appropriate cones in Banach spaces, we derive multiple positive solutions for our boundary value problem.
 1 18 107 . .
2004-03-19 0000-00-00 236 yes 192 no 184 1 2004 9 0 A global bifurcation result of a Neumann problem with indefinite weight
This paper is concerned with the bifurcation result of nonlinear Neumann problem
$$
\left\{\begin{array}{lll}
-\Delta_p u=& \lambda m(x)|u|^{p-2}u + f(\lambda,x,u)& \mbox{in} \ \Omega\\
\frac{\partial u}{\partial \nu}\hspace*{0.55cm}= & 0 & \mbox{on}
\ \partial\Omega.
\end{array}
\right.
$$
We prove that the principal eigenvalue $\lambda_1$ of the corresponding eigenvalue problem with $f\equiv 0,$ is a bifurcation point by using a generalized degree type of Rabinowitz.
 1 14 18 . .
2004-03-31 0000-00-00 186 yes 187 no 187 1 2004 10 0 Oscillation criteria for second order superlinear neutral delay differential equations
New oscillation criteria for the second order nonlinear neutral delay differential equation
$[y(t)+p(t)y(t-\tau )]^{^{\prime \prime}}+q(t)\,f(y(g(t)))=0$, $t\geq t_{0}$
are given. The relevance of our theorems becomes clear due to a carefully selected example.
 1 22 7 . .
2005-05-06 2003-11-03 121 yes 1763 no 186 1 2004 11 0 Fixed points and differential equations with asymptotically constant or periodic solutions
Cooke and Yorke developed a theory of biological growth and epidemics based on an equation $x'(t)=g(x(t))-g(x(t-L))$ with the fundamental property that $g$ is an arbitrary locally Lipschitz function. They proved that each solution either approaches a constant or $\pm \infty$ on its maximal right-interval of definition. They also raised a number of interesting questions and conjectures concerning the determination of the limit set, periodic solutions, parallel results for more general delays, and stability of solutions. Although their paper motivated many subsequent investigations, the basic questions raised seem to remain unanswered.
We study such equations with more general delays by means of two successive applications of contraction mappings. Given the initial function, we explicitly locate the constant to which the solution converges, show that the solution is stable, and show that its limit function is a type of "selective global attractor." In the last section we examine a problem of Minorsky in the guidance of a large ship. Knowledge of that constant to which solutions converge is critical for guidance and control.
 1 31 858 . .
2004-05-28 2004-01-19 857 yes 188 1 2004 12 0 Countably many solutions of a fourth order boundary value problem
We apply fixed point theorems to obtain sufficient conditions for existence of infinitely many solutions of a nonlinear fourth order boundary value problem
$$\displaylines{ u^{(4)}(t) = a(t)f(u(t)), \quad 0 < t < 1, \cr u(0) = u(1) = u'(0) = u'(1) = 0, }$$
where $a(t)$ is $L^p$-integrable and $f$ satisfies certain growth conditions.
 1 15 107 . .
2004-05-29 2004-04-02 237 yes 144 1 2004 13 0 Fredholmness of an abstract differential equation of elliptic type
In this work, we obtain algebraic conditions which assure the Fredholm solvability of an abstract differential equation of elliptic type. In this respect, our work can be considered as an extension of Yakubov's results to the case of boundary conditions containing a linear operator. Although essential technical, this extension is not straight forward as we show it below. The obtained abstract result is applied to a non regular boundary value problem for a second order partial differential equation of an elliptic type in a cylindrical domain. It is interesting to note that the problems considered in cylindrical domains are not coercive.
 1 12 3 . .
2004-06-13 2002-12-06 205 yes 191 1 2004 14 0 On the local integrability and boundedness of solutions to quasilinear parabolic systems
We introduce a structure condition of parabolic type, which allows for the generalization to quasilinear parabolic systems of the known results of integrability, and boundedness of local solutions to singular and degenerate quasilinear parabolic equations.
 1 14 18 . .
2004-09-06 2003-10-01 239 yes 240 no 203 1 2004 15 0 Existence theory for functional initial value problems of ordinary differential equations
In this paper the existence of a solution of general nonlinear functional differential equations is proved under mixed generalized Lipschitz and Carath\'eodory condition. An existence theorem for the extremal solutions is also proved under certain monotonicity and weaker continuity conditions. Examples are provided to illustrate the abstract theory developed in this paper.
 1 14 857 . .
2004-09-18 2004-07-06 2747 yes 204 1 2004 16 0 Asymptotic behavior for minimizers of a p-energy functional associated with p-harmonic map
The author studies the asymptotic behavior of minimizers $u_{\varepsilon}$ of a p-energy functional with penalization as $\varepsilon \to 0$. Several kinds of convergence for the minimizer to the p-harmonic map are presented under different assumptions.
 1 17 22 . .
2004-09-18 2004-02-27 212 yes 207 1 2004 17 0 A fixed point theorem for multivalued mappings
A generalization of the Leray-Schauder principle for multivalued mappings is given. Using this result, an existence theorem for an integral inclusion is obtained.
 1 10 857 . .
2004-11-24 2004-09-05 170 yes 208 1 2004 18 0 Instability of traveling waves for a generalized diffusion model in population problems
In this paper, we study the instability of the traveling waves of a generalized diffusion model in population problems. We prove that some traveling wave solutions are nonlinear unstable under $H^2$ perturbations. These traveling wave solutions converge to a constant as $x\to\infty$.
1 10 25 . .
2004-12-03 2004-03-15 135 yes 209 1 2005 1 0 Existence of global solution for a nonlocal parabolic problem
In this paper, we study a non-local initial boundary-value problem arising in Ohmic heating. By using a dynamical systems approach, some existence and uniqueness results are proved and the existence of a compact attractor is shown.
 1 9 857 . .
2005-02-06 2003-10-27 148 yes 255 no 210 1 2005 2 0 Global existence and asymptotic behaviour for a degenerate diffusive SEIR model
In this paper we analyze the global existence and asymptotic behavior of a reaction diffusion system with degenerate diffusion arising in modeling the spatial spread of an epidemic disease.
 1 15 5 . .
2005-02-06 2004-11-26 1796 yes 257 no 211 1 2005 3 0 Positive solutions for a fourth order boundary value problem
We consider a boundary value problem for the beam equation, in which the boundary conditions mean that the beam is embedded at one end and free at the other end. Some new estimates to the positive solutions to the boundary value problem are obtained. Some sufficient conditions for the existence of at least one positive solution for the boundary value problem are established. An example is given at the end of the paper to illustrate the main results.
 1 17 107 . .
2005-02-17 2004-11-15 241 yes 212 1 2005 4 0 Viscous-inviscid coupled problem with interfacial data
The work presented in this article shows that the viscous/inviscid coupled problem (VIC) has a unique solution when interfacial data are imposed. Domain decomposition techniques and non-uniform relaxation parameters were used to characterize the solution of the new system. Finally, some exact solutions for the VIC problem are provided. These type of solutions are an improvement over those found in recent literatures.
 1 24 16 . .
2005-02-20 2004-12-31 258 yes 213 1 2005 5 0 Asymptotic estimates for PDE with p-Laplacian and damping
We study the positive solutions of equation
\begin{equation*}
\div(\norm{\nabla u}^{p-2}\nabla u)+\ss{\vec b(x)}{\norm{\nabla
u}^{p-2}\nabla u}+c(x)|u|^{q-2}u=0,
\end{equation*}
via the Riccati technique and prove an integral sufficient condition on the potential function $c(x)$ and the damping $\vec b(x)$ which ensures that no positive solution of the equation satisfies a lower (if $p>q$) or upper (if $q>p$) bound eventually.
 1 6 11 . .
2005-02-20 2005-01-06 97 yes 214 1 2005 6 0 Solvability for a nonlinear coupled system of Kirchhoff type for the beam equations with nonlocal boundary conditions
In this paper, we investigate a mathematical model for a nonlinear coupled system of Kirchhoff type of beam equations with nonlocal boundary conditions. We establish existence, regularity and uniqueness of strong solutions. Furthermore, we prove the uniform rate of exponential decay. The uniform rate of polynomial decay is considered.
 1 28 857 . .
2005-04-18 2004-12-03 132 yes 259 no 260 no 261 no 215 1 2005 7 0 A note on the theorem on differential inequalities
It is proved that if a linear operator $\ell:C([a,b];\R)\rightarrow L([a,b];\R)$ is nonpositive and for the initial value problem $$u''(t)=\ell(u)(t)+q(t),\quad u(a)=c_1,\quad u'(a)=c_2 $$ the theorem on {\it differential inequalities} is valid, then $\ell$ is an $a-$Volterra operator.
 1 8 11 . .
2005-04-18 2005-02-07 262 yes 216 1 2005 8 0 The oscillatory behavior of second order nonlinear elliptic equations
Some oscillation criteria are established for the nonlinear damped elliptic differential equation of second order
$$
\sum_{i,\,j=1}^{N}D_i[\,a_{ij}(x)D_jy\,]+\sum_{i=1}^{N}b_i(x)D_iy+p(x)f(y)=0,
\eqno{(E)}
$$
which are different from most known ones in the sense that they are based on a new weighted function $H(r,s,l)$ defined in the sequel. Both the cases when $D_ib_i(x)$ exists for all $i$ and when it does not exist for some $i$ are considered.
 1 11 7 . .
2005-04-20 2004-12-07 263 yes 217 1 2005 9 0 On the exponential convergence to a limit of solutions of perturbed linear Volterra equations
We consider a system of perturbed Volterra integro-differential equations for which the solution approaches a nontrivial limit and the difference between the solution and its limit is integrable. Under the condition that the second moment of the kernel is integrable we show that the solution decays exponentially to its limit if and only if the kernel is exponentially integrable and the tail of the perturbation decays exponentially.
 1 16 857 . .
2005-05-09 2005-01-16 223 yes 264 no 224 no 218 1 2005 10 0 Nonlinear boundary value problem for nonlinear second order differential equations with impulses
The paper deals with the impulsive nonlinear boundary value problem

\begin{displaymath}
u''(t) = f(t,u(t),u'(t)) \quad\mbox{for a.~e.}\ t \in [0,T],
\end{displaymath}
\begin{displaymath}
u(t_j+) = J_j(u(t_j)),\quad u'(t_j+) = M_j(u'(t_j)),\quad j = 1,\ldots,m,
\end{displaymath}
\begin{displaymath}
g_1(u(0),u(T)) = 0, \quad g_2(u'(0),u'(T)) = 0,
\end{displaymath}

where $f \in Car([0,T]\times\rr^{2})$, $g_1$, $g_2 \in C(\rr^2)$, $J_j$, $M_j \in C(\rr)$. An existence theorem is proved for non--ordered lower and upper functions. Proofs are based on the Leray--Schauder degree and on the method of a~priori estimates.
 1 22 11 . .
2005-05-09 2004-10-07 265 yes 219 1 2005 11 0 On a time-dependent subdifferential evolution inclusion with a nonconvex upper-semicontinuous perturbation
We investigate the existence of local approximate and strong solutions for a time-dependent subdifferential evolution inclusion with a nonconvex upper-semicontinuous perturbation.
 1 22 16 . .
2005-05-27 2004-01-22 266 yes 267 no 220 1 2005 12 0 Existence results for impulsive dynamic inclusions on time scales
In this paper, we investigate the existence of solutions and extremal solutions for a first order impulsive dynamic inclusion on time scales. By using suitable fixed point theorems, we study the case when the right hand side has convex as well as nonconvex values.
 1 22 107 . .
2005-05-27 2005-04-08 268 yes 71 no 172 no 221 1 2005 13 0 Oscillation and nonoscillation of perturbed higher order Euler-type differential equations
Oscillatory properties of even order self-adjoint linear differential equations in the form

$$
\sum_{k=0}^{n}
(-1)^k\nu_k\left(\frac{y^{(k)}}{t^{2n-2k-\alpha}}\right)^{(k)}
=(-1)^m\left(q_m(t)y^{(m)}\right)^{(m)},\; \nu_n:=1,
$$

where $m \in \{0, 1\}$, $\alpha \not\in \{1, 3, \dots , 2n-1\}$ and $\nu_0, \dots, \nu_{n-1},$ are real constants satisfying certain conditions, are investigated. In particular, the case when $q_m(t)=\frac{\beta}{t^{2n-2m-\alpha}\ln^2 t }$ is studied.
 1 21 7 . .
2005-06-10 2004-09-10 269 yes 222 1 2005 14 0 On the unique continuation property for a nonlinear dispersive system
We solve the following problem: If $(u,\,v)=(u(x,\,t),\,v(x,\,t))$ is a solution of the Dispersive Coupled System with $t_{1}<t_{2}$ which are sufficiently smooth and such that:
$\,\mbox{supp}\;u(\,.\,,\,t_{j})\subset (a,\,b)\,$
and
$\,\mbox{supp}\;v(\,.\,,\, t_{j})\subset (a,\,b),\,-\,\infty<a<b<\infty ,\,$ $j=1,\,2.\,$
Then $u\equiv 0$ and $v\equiv 0.$
 1 23 857 . .
2005-06-10 2004-09-28 271 yes 270 no 224 1 2005 15 0 Comparison of eigenvalues for a fourth-order four-point boundary value problem
We establish the existence of a smallest eigenvalue for the fourth-order four-point boundary value problem

$\left (\phi_p(u''(t)) \right )'' = \lambda h(t) u(t), \, u'(0) = 0, \,
\beta_0 u(\eta_0) = u(1), \, \phi_p'(u''(0)) = 0, \,
\beta_1\phi_p(u''(\eta_1)) = \phi_p(u''(1))$, $p > 2$,
$0 < \eta_1,\eta_0 < 1, 0 < \beta_1, \beta_0 < 1$,

using the theory of u$_0$-positive operators with respect to a cone in a Banach space. We then obtain a comparison theorem for the smallest positive eigenvalues, $\lambda_1$ and $\lambda_2$, for the differential equations

$\left ( \phi_p(u''(t)) \right )'' = \lambda_1 f(t) u(t)$ and
$\left ( \phi_p(u''(t)) \right )'' =\lambda_2 g(t) u(t)$ where $0 \leq f(t) \leq g(t), t \in [0,1]$.
 1 9 107 . .
2005-07-11 2004-10-12 274 yes 230 no 273 no 225 1 2005 16 0 Oscillation of the solutions of neutral-impulsive differential-difference equations of first order
Sufficient conditions for oscillation of all solutions of a class of neutral impulsive differential-difference equations of first order with deviating argument and fixed moments of impulse effect are found.
 1 11 25 . .
2005-07-11 2004-09-08 276 yes 275 no 226 1 2005 17 0 Existence results for nondensely defined semilinear functional differential inclusions in Fréchet spaces
In this paper, a recent Frigon nonlinear alternative for contractive multivalued maps in Fr\'echet spaces, combined with semigroup theory, is used to investigate the existence of integral solutions for first order semilinear functional differential inclusions. An application to a control problem is studied. We assume that the linear part of the differential inclusion is a nondensely defined operator and satisfies the Hille-Yosida condition.
 1 17 107 . .
2005-08-22 2005-06-06 57 yes 172 no 228 1 2005 18 0 Existence of solutions to nonlocal and singular variational elliptic inequality via Galerkin method
In this article, we study the existence of solutions for nonlocal variational elliptic inequality
$$ -M(\|u\|^2)\Delta u \geq f(x,u) $$
Making use of the penalized method and Galerkin approximations, we establish existence theorems for both cases when $M$ is continuous and when $M$ is discontinuous.
 1 12 857 . .
2005-08-30 2004-12-12 280 yes 218 no 227 1 2005 19 0 Remarks on inhomogeneous elliptic problems arising in astrophysics
We deal with the variational study of some type of nonlinear inhomogeneous elliptic problems arising in models of solar flares on the halfplane $\R$.
 1 12 24 . .
2005-09-15 2000-10-23 278 yes 279 no 230 1 2005 20 0 Spatial analyticity of solutions of a nonlocal perturbation of the KdV equation
Let $\H$ denote the Hilbert transform and $\eta \ge 0$. We show that if the initial data of the following problems

$ u_t + u u_x + u_{xxx} + \eta(\mathcal{H} u_x + \mathcal{H} u_{xxx}) = 0, \,
u(\cdot , 0) = \phi (\cdot)$ and
$ v_t + \frac{1}{2} (v_x)^2 + v_{xxx} + \eta(\mathcal{H} v_x + \mathcal{H} v_{xxx}) = 0, \,
v(\cdot , 0) = \psi (\cdot)$

has an analytic continuation to a strip containing the real axis, then the solution has the same property, although the width of the strip might diminish with time. When $\eta>0$ and the initial data is complex-valued we prove local well-posedness of the two problems above in spaces of analytic functions, which implies the constancy over time of the radius of the strip of analyticity in the complex plane around the real axis.
 1 21 8 . .
2005-11-05 2004-05-13 282 yes 232 1 2005 21 0 First order integro-differential equations in Banach algebras involving Caratheodory and discontinuous nonlinearities
In this paper some existence theorems for the first order differential equations in Banach algebras is proved under the mixed generalized Lipschitz, Carath\'eodory and monotonicity conditions.
 1 16 107 . .
2005-11-05 2005-06-30 2747 yes 284 no 233 1 2005 22 0 Existence of solutions for nonconvex third order differential inclusions
This paper proves the existence of solutions for a third order initial value nonconvex differential inclusion. We start with an upper semicontinuous compact valued multifunction \emph{F} which is contained in a lower semicontinuous convex function $\partial V$ and show that,

$x^{(3)}(t) \in F(x(t),x'(t),x''(t)),$ $ \: x(0)=x_{0}, \: x'(0)=y_{0}, \: x''(0)=z_{0}$.
 1 11 107 . .
2005-11-05 2005-09-16 283 yes 231 1 2005 23 0 Oscillation of second-order forced nonlinear dynamic equations on time scales
In this paper, we discuss the oscillatory behavior of the second-order forced nonlinear dynamic equation
\begin{equation*}
\left( a(t)x^{\Delta }(t)\right) ^{\Delta }+p(t)f(x^{\sigma })=r(t),
\end{equation*}%
on a time scale ${\mathbb{T}}$ when $a(t)>0$. We establish some sufficient conditions which ensure that every solution oscillates or satisfies $\lim \inf_{t\rightarrow \infty }\left\vert x(t)\right\vert =0.$ Our oscillation results when $r(t)=0$ improve the oscillation results for dynamic equations on time scales that has been established by Erbe and Peterson [Proc. Amer. Math. Soc \ 132 (2004), 735-744], Bohner, Erbe and Peterson [J. Math. Anal. Appl. 301 (2005), 491--507] since our results do not require $% \int_{t_{0}}^{\infty }q(t)\Delta t>0$ and $\int_{\pm t_{0}}^{\pm \infty }% \frac{du}{f(u)}<\infty .$ Also, as a special case when ${\mathbb{T=R}}$, and $r(t)=0$ our results improve some oscillation results for differential equations. Some examples are given to illustrate the main results.
 1 17 71 . .
2005-11-05 2005-07-21 121 yes 234 1 2005 24 0 On the uniform boundedness of the solutions of systems of reaction-diffusion equations
We consider a system of reaction-diffusion equations for which the uniform boundedness of the solutions can not be derived by existing methods. The system may represent, in particular, an epidemic model describing the spread of an infection disease within a population. We present an $L^{p}$ argument allowing to establish the global existence and the uniform boundedness of the solutions of the considered system.
 1 10 71 . .
2005-12-21 2005-07-01 285 yes 286 no 287 no 235 1 2005 25 0 An existence result of asymptotically stable solutions for an integral equation of mixed type
In the present Note an existence result of asymptotically stable solutions for the integral equation
$$
x\left( t\right) =q\left( t\right) +\int_{0}^{t}K\left( t,s,x\left( s\right) \right) ds
+\int_{0}^{\infty }G\left( t,s,x\left( s\right) \right) ds
$$
is presented.
 1 6 857 . .
2005-12-30 2005-11-03 170 yes 171 no 236 1 2005 26 0 Boundedness and stability in nonlinear delay difference equations employing fixed point theory
In this paper we study stability and boundedness of the nonlinear difference equation
\begin{equation} x(t+1)=a(t)x(t)+c(t)\Delta x(t-g(t))+q(x(t),x(t-g(t))\big).\nonumber \end{equation}
In particular we study equi-boundedness of solutions and the stability of the zero solution of this equation. Fixed point theorems are used in the analysis.
 1 18 857 . .
2005-12-30 2005-12-16 114 yes 288 no 237 1 2006 1 0 Attractors for a class of doubly nonlinear parabolic systems
In this paper, we establish the existence and boundedness of solutions of a doubly nonlinear parabolic system. We also obtain the existence of a global attractor and the regularity property for this attractor in $\left[ L^{\infty }(\Omega )\right] ^{2}$ and
${\displaystyle \prod_{i=1}^{2}}{B_{\infty }^{1+\sigma _{i},p_{i}}( \Omega )} $.
 1 15 16 . .
2006-03-15 2004-04-19 149 yes 148 no 238 1 2006 2 0 Integral equations, Volterra equations, and the remarkable resolvent: contractions
This paper concerns several variants of an integral equation
$$ x(t)=a(t)-\int^t_0 C(t,s) x(s)ds $$, a resolvent $$ R(t,s) $$, and a variation-of-parameters formula
$$ x(t)=a(t)-\int^t_0 R(t,s) a(s)ds $$ with special accent on the case in which $a(t)$ is unbounded. We use contraction mappings to establish close relations between $a(t)$ and $\int^t_0R(t,s) a(s)ds$.
 1 17 107 . .
2006-03-28 2006-02-25 857 yes 239 1 2006 3 0 An application of the antimaximum principle for a fourth order periodic problem
We study the existence of solutions for a periodic fourth order problem. We prove an associated uniform antimaximum principle and develop a method of upper and lower solutions in reversed order. Furthermore, by the quasilinearization method we construct an iterative sequence that converges quadratically to a solution.
 1 12 857 . .
2006-04-14 2005-05-16 289 yes 290 no 240 1 2006 4 0 A class of second order BVPs on infinite intervals
In this work, we are concerned with a boundary value problem associated with a generalized Fisher-like equation. This equation involves an eigenvalue and a parameter which may be viewed as a wave speed. According to the behavior of the nonlinear source term, existence results of bounded solutions, positive solutions, classical as well as weak solutions are provided. We mainly use fixed point arguments.
 1 19 107 . .
2006-05-05 2006-02-19 1008 yes 1207 no 241 1 2006 5 0 Renormalized solutions of a nonlinear parabolic equation with double degeneracy
In this paper, we consider the initial-boundary value problem of a nonlinear parabolic equation with double degeneracy, and establish the existence and uniqueness theorems of renormalized solutions which are stronger than $BV$ solutions.
 1 12 19 . .
2006-06-05 2005-12-30 1569 yes 294 no 293 no 242 1 2006 6 0 The shooting method and multiple solutions of two/multi-point BVPs of second-order ODE
Within the last decade, there has been growing interest in the study of multiple solutions of two- and multi-point boundary value problems of nonlinear ordinary differential equations as fixed points of a cone mapping. Undeniably many good results have emerged. The purpose of this paper is to point out that, in the special case of second-order equations, the shooting method can be an effective tool, sometimes yielding better results than those obtainable via fixed point techniques.
 1 14 857 . .
2006-06-05 2006-05-12 295 yes 243 1 2006 7 0 Positive solutions of second order boundary value problems with changing signs Carathéodory nonlinearities
In this paper we investigate the existence of positive solutions of two-point boundary value problems for nonlinear second order differential equations of the form $(py^{\prime})^{\prime}(t)+q(t)y(t)=f(t,y(t),y^{\prime}(t))$, where $f$ \ is a Carath\'{e}odory function, which may change sign, with respect to its second argument, infinitely many times.
 1 14 107 . .
2006-06-05 2005-12-05 296 yes 57 no 244 1 2006 8 0 On singular solutions of a second order differential equation
In the paper, sufficient conditions are given under which all nontrivial solutions of $(g(a(t)y'))' + r(t) f (y) = 0$ are proper where $a>0, r>0, f(x) x>0, g(x) x>0$ for $x\ne0$ and $g$ is increasing on $R$. A sufficient condition for the existence of a singular solution of the second kind is given.
 1 13 7 . .
2006-06-20 2006-03-08 297 yes 247 1 2006 9 0 On the iterated order and the fixed points of entire solutions of some complex linear differential equations
In this paper, we investigate the iterated order of entire solutions of homogeneous and non-homogeneous linear differential equations with entire coefficients.
 1 11 107 . .
2006-07-18 2006-04-02 1377 yes 246 1 2006 10 0 Integral criteria for second-order linear oscillation
We present several new criteria for the oscillation of the second-order linear equation $ y''(t)+q(t)y(t)=0 $, in which the coefficient $ q $ may or may not change signs. The criteria involve the integral $ \int t^\gamma q(t)\, dt $ for some $ \gamma >0 $. The special case $ \gamma =2 $ is then studied in greater details.
 1 18 857 . .
2006-07-18 2006-05-26 295 yes 249 1 2006 11 0 Boundary value problems for doubly perturbed first order ordinary differential systems
The aim of this paper is to present new results on existence theory for perturbed BVPs for first order ordinary differential systems. A nonlinear alternative for the sum of a contraction and a compact mapping is used.
 1 10 107 . .
2006-08-05 2005-12-11 71 yes 1008 no 1207 no 250 1 2006 12 0 Localized solutions of elliptic equations: loitering at the hilltop
We find an infinite number of smooth, localized, radial solutions of $\Delta_{p} u + f(u) = 0$ in ${\Bbb R}^{N}$ - one with each prescribed number of zeros - where $\Delta_{p}u$ is the $p$-Laplacian of the function $u$.
 1 15 20 . .
2006-08-05 2006-06-06 130 yes 251 1 2006 13 0 New existence theorems of positive solutions for singular boundary value problems
In this paper, some nonexistence, existence and multiplicity of positive solutions are established for a class of singular boundary value problem. The authors also obtain the relation between the existence of the solutions and the parameter $\lambda$. The arguments are based upon the fixed point index theory and the upper and lower solutions method.
 1 9 13 . .
2006-08-08 2006-06-22 299 yes 301 no 300 no 252 1 2006 14 0 Principal matrix solutions and variation of parameters for a Volterra integro-differential equation and its adjoint
We define the principal matrix solution $Z(t,s)$ of the linear Volterra vector integro-differential equation
\[ x'(t) = A(t)x(t) + \int_s^t B(t,u)x(u)\,du \]
in the same way that it is defined for $x' = A(t)x$ and prove that it is the unique matrix solution of
\[ \frac{\partial}{\partial{t}}Z(t,s) = A(t)Z(t,s) + \int_{s}^t B(t,u)Z(u,s)\,du, \quad Z(s,s) = I. \]
Furthermore, we prove that the solution of
\[ x'(t) = A(t)x(t) + \int_{\tau}^t B(t,u)x(u)\,du + f(t), \quad x(\tau) = x_0\]
is unique and given by the variation of parameters formula
\[ x(t) = Z(t,\tau)x_0 + \int_{\tau}^t Z(t,s)f(s)\,ds.\]
We also define the principal matrix solution $R(t,s)$ of the adjoint equation
\[ r'(s) = -r(s)A(s) - \int_s^t r(u)B(u,s)\,du \]
and prove that it is identical to Grossman and Miller's resolvent, which is the unique matrix solution of
\[ \frac{\partial}{\partial{s}}R(t,s) = -R(t,s)A(s) - \int_{s}^t R(t,u)B(u,s)\,du, \quad R(t,t) = I. \]
Finally, we prove that despite the difference in their definitions $R(t,s)$ and $Z(t,s)$ are in fact identical.
 1 22 857 . .
2006-08-23 2006-08-11 302 yes 254 1 2006 15 0 Monotone increasing multi-valued condensing random operators and random differential inclusions
In this paper, some random fixed point theorems for monotone increasing, condensing and closed multi-valued random operators are proved. They are then applied to first order ordinary nonconvex random differential inclusions for proving the existence of solutions as well as the existence of extremal solutions under certain monotonicity conditions.
 1 20 7 . .
2006-10-13 2006-07-26 2747 yes 70 no 298 no 255 1 2006 16 0 Almost automorphic mild solutions to some semilinear abstract differential equations with deviated argument in Fréchet spaces
In this paper we consider the semilinear differential equation with deviated argument in a Fr\'echet space $x^{\prime}(t) = A x(t) + f(t, x(t), x[\alpha(x(t),t)]),$ $t \in {\mathbb{R}}$, where $A$ is the infinitesimal (bounded) generator of a $C_{0}$-semigroup satisfying some conditions of exponential stability. Under suitable conditions on the functions $f$ and $\alpha$ we prove the existence and uniqueness of an almost automorphic mild solution to the equation.
 1 8 8 . .
2006-10-24 2006-01-26 303 yes 256 1 2006 17 0 A note on the existence of solutions to some nonlinear functional integral equations
Substituting the usual growth condition by an assumption that a specific initial value problem has a maximal solution, we obtain existence results for functional nonlinear integral equations with variable delay. Application of the technique to initial value problems for differential equations as well as to integrodifferential equations are given.
 1 24 857 . .
2006-10-24 2006-08-17 304 yes 257 1 2006 18 0 Location of resonances generated by degenerate potential barrier
We study resonances of the semi-classical Schr\"odinger operator $H = -h^2 \Delta + V$ on $L^2( \R^N)$. We consider the case where the potential $V$ have an absolute degenerate maximum. Then we prove that $H$ has resonances with energies $E = V_0 + e^{-i {\pi \over \sigma +1}} h^{ 2 \sigma \over \sigma +1} k_j + {\cal O}( h^{ 2 \sigma +1 \over \sigma +1} ),$ where $k_j $ is in the spectrum of some quartic oscillator.
 1 11 107 . .
2006-10-24 2006-05-21 305 yes 306 no 253 1 2006 19 0 Quasilinear degenerated equations with L^1 datum and without coercivity in perturbation terms
In this paper we study the existence of solutions for the generated boundary value problem, with initial datum being an element of $L^1(\Omega)+W^{-1, p'}(\Omega, w^{*})$

$$-{\rm div}a(x, u, \nabla u) + g(x, u, \nabla u) = f-{\rm div}F $$

where $a(.)$ is a Carath\'eodory function satisfying the classical condition of type Leray-Lions hypothesis, while $g(x, s, \xi)$ is a non-linear term which has a growth condition with respect to $\xi$ and no growth with respect to $s$, but it satisfies a sign condition on $s$.
 1 18 16 . .
2006-11-15 2005-10-15 180 yes 181 no 179 no 258 1 2006 20 0 Stability of Volterra difference delay equations
We study the asymptotic stability of the zero solution of the Volterra difference delay equation

\begin{equation}
x(n+1)=a(n)x(n)+c(n)\Delta x(n-g(n))+\sum^{n-1}_{s=n-g(n)}k(n,s)h(x(s)).\nonumber
\end{equation}

A Krasnoselskii fixed point theorem is used in the analysis.
 1 14 857 . .
2006-11-23 2006-08-18 288 yes 259 1 2007 1 0 An extended method of quasilinearization for nonlinear impulsive differential equations with a nonlinear three-point boundary condition
In this paper, we discuss an extended form of generalized quasilinearization technique for first order nonlinear impulsive differential equations with a nonlinear three-point boundary condition. In fact, we obtain monotone sequences of upper and lower solutions converging uniformly and quadratically to the unique solution of the problem.
 1 19 107 . .
2007-01-26 2006-09-19 307 yes 308 no 260 1 2007 2 0 On the existence of mild solutions for neutral functional differential inclusions in Banach space
A theorem on existence of mild solutions for partial neutral functional differential inclusions with unbounded linear part generating a noncompact semigroup in Banach space is established.
 1 15 70 . .
2007-01-29 2006-04-14 309 yes 261 1 2007 3 0 Existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations
The paper examines the existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations. Namely, some sufficient conditions for the existence and uniqueness of pseudo almost periodic solutions to those classes of hyperbolic evolution equations are given. As an application, we consider the existence of pseudo almost periodic solutions to the heat equations with delay.
 1 12 70 . .
2007-02-05 2006-08-06 947 yes 264 1 2007 4 0 Positive solutions to an Nth order right focal boundary value problem
The existence of a positive solution is obtained for the $n^{th}$ order right focal boundary value problem $y^{(n)}=f(x,y)$, $0 < x \leq 1$, $y^{(i)}(0)=y^{(n-2)}(p)=y^{(n-1)}(1)=0, i=0,\cdots, n-3$, where $\frac{1}{2}<p<1$ is fixed and where $f(x,y)$ is singular at $x=0, y=0$, and possibly at $y=\infty$. The method applies a fixed-point theorem for mappings that are decreasing with respect to a cone.
 1 17 107 . .
2007-03-02 2006-06-22 313 yes 265 1 2007 5 0 On existence of proper solutions of quasilinear second order differential equations
In the paper, the nonlinear differential equation $(a(t)|y^{\prime}|^{p-1}y^{\prime})^{\prime}+b(t)g(y^{\prime})+r(t)f(y)=e(t)$ is studied. Sufficient conditions for the nonexistence of singular solutions of the first and second kind are given. Hence, sufficient conditions for all nontrivial solutions to be proper are derived. Sufficient conditions for the nonexistence of weakly oscillatory solutions are given.
 1 14 7 . .
2007-03-12 2006-12-15 297 yes 314 no 263 1 2007 6 0 On the stability of some fractional-order non-autonomous systems
The fractional calculus (integration and differentiation of fractional-order) is a one of the singular integral and integro-differential operators. In this work a class of fractional-order non-autonomous systems will be considered. The stability (and some other properties concerning the existence and uniqueness) of the solution will be proved.
 1 14 857 . .
2007-03-12 2006-12-12 311 yes 312 no 266 1 2007 7 0 Viability problem with perturbation in Hilbert space
This paper deals with the existence result of viable solutions of the differential inclusion \begin{center}$\dot{x}(t) \in f(t,x(t)) + F(x(t))$\\$x(t) \in K$ on $[0,T],$ \end{center} where $K$ is a locally compact subset in separable Hilbert space $H,$ $(f(s,\cdot))_s$ is an equicontinuous family of measurable functions with respect to $s$ and $F$ is an upper semi-continuous set-valued mapping with compact values contained in the Clarke subdifferential $\partial_{c} V(x)$ of an uniformly regular function $V.$
 1 14 70 . .
2007-03-25 2006-11-27 315 yes 316 no 267 1 2007 8 0 On the existence of solutions for a higher order differential inclusion without convexity
We prove a Filippov type existence theorem for solutions of a higher order differential inclusion in Banach spaces with nonconvex valued right hand side by applying the contraction principle in the space of the derivatives of solutions instead of the space of solutions.
 1 8 70 . .
2007-03-25 2006-12-16 317 yes 269 1 2007 9 0 Global solutions and exponential decay for a nonlinear coupled system of beam equations of Kirchhoff type with memory in a domain with moving boundary
In this paper we prove the exponential decay in the case $n>2$, as time goes to infinity, of regular solutions for a nonlinear coupled system of beam equations of Kirchhoff type with memory and weak damping
\begin{eqnarray*}
&&u_{tt}+\Delta^2 u-M(||\nabla u||^2_{L^2(\Omega_t)}+||\nabla
v||^2_{L^2(\Omega_t)})\Delta u\\
&&+\int^{t}_{0}g_1(t-s)\Delta u(s)ds
+\alpha u_{t}+h(u-v)=0 \quad \mbox{in} \quad \hat{Q},\\
&&v_{tt}+\Delta^2 v-M(||\nabla u||^2_{L^2(\Omega_t)}+||\nabla
v||^2_{L^2(\Omega_t)})\Delta v \\
&&+\int^{t}_{0}g_2(t-s)\Delta v(s)ds + \alpha v_{t}-h(u-v)=0 \quad
\mbox{in} \quad \hat{Q}
\end{eqnarray*}
in a non cylindrical domain of $\R^{n+1}$ $(n\ge1)$ under suitable hypothesis on the scalar functions $M$, $h$, $g_1$ and $g_2$, and where $\alpha$ is a positive constant. We show that such dissipation is strong enough to produce uniform rate of decay. Besides, the coupling is nonlinear which brings up some additional difficulties, which plays the problem interesting. We establish existence and uniqueness of regular solutions for any $n\ge 1$.
 1 24 857 . .
2007-04-21 2006-10-04 132 yes 321 no 268 1 2007 10 0 Global exponential stability of impulsive dynamical systems with distributed delays
In this paper, the global exponential stability of dynamical systems with distributed delays and impulsive effect is investigated. By establishing an impulsive differential-integro inequality, we obtain some sufficient conditions ensuring the global exponential stability of the dynamical system. Three examples are given to illustrate the effectiveness of our theoretical results.
 1 13 857 . .
2007-04-21 2005-10-21 318 yes 319 no 320 no 270 1 2007 11 0 q-Dominant and q-recessive matrix solutions for linear quantum systems
In this study, linear second-order matrix $q$-difference equations are shown to be formally self-adjoint equations with respect to a certain inner product and the associated self-adjoint boundary conditions. A generalized Wronskian is introduced and a Lagrange identity and Abel's formula are established. Two reduction-of-order theorems are given. The analysis and characterization of $q$-dominant and $q$-recessive solutions at infinity are presented, emphasizing the case when the quantum system is disconjugate.
 1 29 107 . .
2007-05-25 2007-03-15 322 yes 323 no 271 1 2007 12 0 Uniform continuity of the solution map for nonlinear wave equation in Reissner-Nordstrom metric
In this paper we study the properties of the solutions to the Cauchy problem
$$
(u_{tt}-\Delta u)_{g_s}=f(u)+g(|x|),\quad t\in [0, 1], x\in {\cal R}^3,
\leqno{(1)}
$$
$$
u(1, x)=u_0\in {\dot H}^1({\cal R}^3),\quad
u_t(1, x)=u_1\in L^2({\cal R}^3),
\leqno{(2)}
$$
where $g_s$ is the Reissner-Nordstr${\ddot o}$m metric (see [2]); $f\in {\cal C}^1({\cal R}^1)$, $f(0)=0$, $a|u|\leq f'(u)\leq b|u|$, $g\in {\cal C}({\cal R}^+)$, $g(|x|)\geq 0$, $g(|x|)=0$ for $|x|\geq r_1$, $a$ and $b$ are positive constants, $r_1>0$ is suitable chosen. When $g(r)\equiv 0$ we prove that the Cauchy problem $(1)$, $(2)$ has a nontrivial solution $u(t, r)$ in the form $u(t, r)=v(t)\omega(r)\in {\cal C}((0, 1]{\dot H}^1({\cal R}^+))$, where $r=|x|$, and the solution map is not uniformly continuous. When $g(r)\ne 0$ we prove that the Cauchy problem $(1)$, $(2)$ has a nontrivial solution $u(t, r)$ in the form $u(t, r)=v(t)\omega(r)\in {\cal C}((0, 1]{\dot H}^1({\cal R}^+))$, where $r=|x|$, and the solution map is not uniformly continuous.
 1 14 11 . .
2007-07-07 2007-04-23 110 yes 272 1 2007 13 0 Computation of radial solutions of semilinear equations
We express radial solutions of semilinear elliptic equations on $R^n$ as convergent power series in $r$, and then use Pade approximants to compute both ground state solutions, and solutions to Dirichlet problem. Using a similar approach we have discovered existence of singular solutions for a class of subcritical problems. We prove convergence of the power series by modifying the classical method of majorants.
 1 14 79 . .
2007-07-07 2007-03-29 51 yes 274 1 2007 14 0 Solution to a transmission problem for quasilinear pseudoparabolic equations by the Rothe method
In this paper, we deal with a transmission problem for a class of quasilinear pseudoparabolic equations. Existence, uniqueness and continuous dependence of the solution upon the data are obtained via the Rothe method. Moreover, the convergence of the method and an error estimate of the approximations are established.
 1 27 71 . .
2007-07-25 2006-10-10 2235 yes 325 no 273 1 2007 15 0 Functional differential inclusions with integral boundary conditions
In this paper, we investigate the existence of solutions for a class of second order functional differential inclusions with integral boundary conditions. By using suitable fixed point theorems, we study the case when the right hand side has convex as well as nonconvex values.
1 13 107 . .
2007-07-25 2006-11-11 71 yes 326 no 57 no 276 1 2007 16 0 Positive periodic solutions in neutral nonlinear differential equations
We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral differential equation with delay
\begin{equation}
\frac{d}{dt}[x(t) - ax(t-\tau)]= r(t)x(t)- f(t, x(t-\tau))
\end{equation}
has a positive periodic solution. An example will be provided as an application to our theorems.
 1 10 3 . .
2007-09-05 2007-07-01 113 yes 275 1 2007 17 0 Hybrid approximations via second order combined dynamic derivatives on time scales
This article focuses on the approximation of conventional second order derivative via the combined (diamond-$\alpha$) dynamic derivative on time scales with necessary smoothness conditions embedded. We will show the constraints under which the second order dynamic derivative provides a consistent approximation to the conventional second derivative; the cases where the dynamic derivative approximates the derivative only via a proper modification of the existing formula; and the situations in which the dynamic derivative can never approximate consistently even with the help of available structure correction methods. Constructive error analysis will be given via asymptotic expansions for practical hybrid modeling and computational applications.
 1 13 107 . .
2007-09-12 2007-06-18 327 yes 277 1 2007 18 0 Positive solutions for systems of nth order three-point nonlocal boundary value problems
Intervals of the parameter $\lambda$ are determined for which there exist positive solutions for the system of nonlinear differential equations, $u^{(n)} + \lambda a(t) f(v) = 0, \ v^{(n)} +\lambda b(t) g(u) = 0, $ for $0 < t <1$, and satisfying three-point nonlocal boundary conditions, $u(0) = 0, u'(0) = 0, \ldots, u^{(n-2)}(0) = 0, \ u(1)=\alpha u(\eta), v(0) = 0, v'(0) = 0, \ldots, v^{(n-2)}(0) = 0, \ v(1)=\alpha v(\eta)$. A Guo-Krasnosel'skii fixed point theorem is applied.
 1 12 107 . .
2007-09-12 2007-06-12 57 yes 70 no 278 1 2007 19 0 Null controllability of some impulsive evolution equation in a Hilbert space
We shall establish a necessary and sufficient condition under which we have the null controllability of some first order impulsive evolution equation in a Hilbert space.
 1 21 71 . .
2007-10-05 2006-10-17 328 yes 164 no 279 1 2007 20 0 On rectifiable oscillation of Euler type second order linear differential equations
We study the oscillatory behavior of solutions of the second order linear differential equation of Euler type: $(E)\ y'' + \lambda x^{-\alpha} y = 0, \ x \in (0, 1]$, where $\lambda > 0$ and $\alpha> 2$. Theorem (a) For $2 \le \alpha < 4$, all solution curves of $(E)$ have finite arc length; (b) For $\alpha \ge 4$, all solution curves of $(E)$ have infinite arc length. This answers an open problem posed by M. Pasic [8]
 1 12 858 . .
2007-10-08 2007-04-16 330 yes 280 1 2007 21 0 On global attractivity of solutions of a functional-integral equation
We prove an existence theorem for a quadratic functional-integral equation of mixed type. The functional-integral equation studied below contains as special cases numerous integral equations encountered in nonlinear analysis. With help of a suitable measure of noncompactness, we show that the functional integral equation of mixed type has solutions being continuous and bounded on the interval $[0,\infty)$ and those solutions are globally attractive.
 1 10 857 . .
2007-10-08 2007-07-23 47 yes 281 1 2007 22 0 On the existence of solutions to some nonlinear integrodifferential equations with delays
Existence of solutions to some nonlinear integral equations with variable delays are obtained by the use of a fixed point theorem due to Dhage. As applications of the main results, existence results to some initial value problems concerning differential equations of higher order as well as integro-differential equations are derived. The case of Lipschitz-type conditions is also considered. Our results improve and generalize, in several ways, existence results already appeared in the literature.
 1 21 857 . .
2007-10-20 2007-05-03 304 yes 282 1 2007 23 0 Sufficient condition for existence of solutions for higher-order resonance boundary value problem with one-dimensional p-Laplacian
By using coincidence degree theory of Mawhin, existence results for some higher order resonance multipoint boundary value problems with one dimensional p-Laplacian operator are obtained.
 1 11 16 . .
2007-10-22 2007-04-27 331 yes 332 no 333 no 283 1 2007 24 0 Existence of a solution for a class of nonlinear parabolic systems
An existence result of a solution for a class of nonlinear parabolic systems is established. The data belong to $L^1$ and no growth assumption is made on the nonlinearities.
 1 18 16 . .
2007-10-22 2006-05-03 334 yes 284 1 2007 25 0 Oscillation of second-order nonlinear differential equations with damping term
We present new oscillation criteria for the second order nonlinear differential equation with damping term of the form
\begin{equation*}
\left( r(t)\psi (x)f(\dot{x})\right) ^{\cdot }+p(t)\varphi \left(g(x),r(t)\psi(x)f(\dot{x})\right)+q(t)g(x)=0,
\end{equation*}
where $p$, $q$, $r:[t_{o},\infty )\rightarrow \mathbf{R}$ and\ $\psi $, $g $, $f:\mathbf{R}\rightarrow \mathbf{R}$ are continuous, $r(t)>0$,\ $p(t)\geq 0$ and $\psi (x)>0$, $xg(x)>0$ for $x\neq 0$, $uf(u)>0$ for $u\neq0 $. Our results generalize and extend some known oscillation criteria in the literature. The relevance of our results is illustrated with a number of examples.
 1 19 857 . .
2007-11-05 2006-09-19 335 yes 336 no 285 1 2007 26 0 Existence of positive solutions for multi-point boundary value problems
The existence of positive solutions are established for the multi-point boundary value problems
$$
\left\{ \begin{array}{ll}
(-1)^nu^{(2n)}(x)=\lambda p(x)f(u(x)), \hspace*{.2in} 0<x<1 \\
u^{(2i)}(0)=\sum_{j=1}^{m}a_ju^{(2i)}(\eta _j), \quad
u^{(2i+1)}(1)=\sum_{j=1}^{m}b_ju^{(2i+1)}(\eta _j), \quad i=0, 1,
\ldots , n-1
\end{array} \right.
$$
where $a_j,b_j\in[0,\infty), \ j=1, 2, \ldots, m,$ with $0<\sum_{j=1}^{m}a_j<1, \ 0<\sum_{j=1}^{m}b_j<1,$ and $ \eta_j \in(0,1)$ with $0<\eta_1<\eta_2<\ldots <\eta_m<1,$ under certain conditions on $f$ and $p$ using the Krasnosel'skii fixed point theorem for certain values of $\l$. We use the positivity of the Green's function and cone theory to prove our results.
 1 11 107 . .
2007-11-05 2007-07-30 274 yes 337 no 286 1 2007 27 0 Nonlinear parabolic problems with Neumann-type boundary conditions and L^1-data
In this paper, we study existence, uniqueness and stability questions for the nonlinear parabolic equation:
$$ \frac{\partial u}{\partial t}-\triangle_{p}u+\alpha(u)=f in ]0,\ T[\times\Omega, $$ with Neumann-type boundary conditions and initial data in $L^1$. Our approach is based essentially on the time discretization technique by Euler forward scheme.
 1 22 71 . .
2007-11-15 2006-08-06 148 yes 338 no 287 1 2007 28 0 On the approximation of the limit cycles function
We consider planar vector fields depending on a real parameter. It is assumed that this vector field has a family of limit cycles which can be described by means of the limit cycles function $l$. We prove a relationship between the multiplicity of a limit cycle of this family and the order of a zero of the limit cycles function. Moreover, we present a procedure to approximate $l(x)$, which is based on the Newton scheme applied to the Poincar\'e function and represents a continuation method. Finally, we demonstrate the effectiveness of the proposed procedure by means of a Li\'enard system.
 1 11 858 . .
2007-11-19 2007-04-11 339 yes 340 no 341 no 289 1 2007 29 0 On the existence of a component-wise positive radially symmetric solution for a superlinear system
The system under consideration is
$$
-\Delta u+a_uu=u^3-\beta uv^2, \quad u=u(x),
$$
$$
-\Delta v+a_vv=v^3-\beta u^2v, \quad v=v(x), \ x\in \mathbb {R}^3,
$$
$$
u\big| _{|x|\to \infty }=v\big| _{|x|\to \infty }=0,
$$
where $a_u,a_v$ and $\beta $ are positive constants. We prove the existence of a component-wise positive smooth radially symmetric solution of this system. This result is a part of the results presented in the recent paper by Sirakov [1]; in our opinion, our method allows one to treat the problem simpler and shorter.
 1 7 79 . .
2007-12-06 2007-09-19 342 yes 288 1 2007 30 0 Weighted Cauchy-type problem of a functional differ-integral equation
In this work, we are concerned with a nonlinear weighted Cauchy type problem of a differ-integral equation of fractional order. We will prove some local and global existence theorems for this problem, also we will study the uniqueness and stability of its solution.
 1 9 857 . .
2007-12-06 2007-07-15 312 yes 311 no 291 1 2008 1 0 Positive solutions of boundary value problems for nth order ordinary differential equations
In this paper, we investigate the problem of existence and nonexistence of positive solutions for the nonlinear boundary value problem:

\begin{eqnarray*}
u^{(n)}(t)+\lambda a(t)f(u(t))=0,\,\,\, 0<t<1,
\end{eqnarray*}

satisfying three kinds of different boundary value conditions. Our analysis relies on Krasnoselskii's fixed point theorem of cone. An example is also given to illustrate the main results.
 1 9 107 . .
2008-01-07 2007-08-20 344 yes 292 1 2008 2 0 Integral equations with contrasting kernels
In this paper we study integral equations of the form $x(t)=a(t)-\int^t_0 C(t,s)x(s)ds$ with sharply contrasting kernels typified by $C^*(t,s)=\ln (e+(t-s))$ and $D^*(t,s)=[1+(t-s)]^{-1}$. The kernel assigns a weight to $x(s)$ and these kernels have exactly opposite effects of weighting. Each type is well represented in the literature. Our first project is to show that for $a\in L^2[0,\infty)$, then solutions are largely indistinguishable regardless of which kernel is used. This is a surprise and it leads us to study the essential differences. In fact, those differences become large as the magnitude of $a(t)$ increases.

The form of the kernel alone projects necessary conditions concerning the magnitude of $a(t)$ which could result in bounded solutions. Thus, the next project is to determine how close we can come to proving that the necessary conditions are also sufficient.

The third project is to show that solutions will be bounded for given conditions on $C$ regardless of whether $a$ is chosen large or small; this is important in real-world problems since we would like to have $a(t)$ as the sum of a bounded, but badly behaved function, and a large well behaved function.
1 22 25 . .
2008-01-07 2007-08-31 857 yes 293 1 2008 3 0 Positive solutions of a boundary value problem for a nonlinear fractional differential equation
In this paper we give sufficient conditions for the existence of at least one and at least three positive solutions to the nonlinear fractional boundary value problem

\begin{eqnarray*}
&&D^{\alpha}u + a(t) f(u) = 0, \quad 0<t<1, 1<\alpha\leq2,\\
&&u(0) = 0 ,u'(1)= 0,
\end{eqnarray*}

where $ D^{\alpha}$ is the Riemann-Liouville differential operator of order $\alpha $, $f: [0,\infty)\rightarrow [0,\infty)$ is a given continuous function and $a$ is a positive and continuous function on $[0,1]$.
 1 11 107 . .
2008-01-07 2007-07-30 230 yes 345 no 294 1 2008 4 0 Existence and uniqueness of a solution to a partial integro-differential equation by the method of lines
In this work we consider a partial integro-differential equation. We reformulate it a functional integro-differential equation in a suitable Hilbert space. We apply the method of lines to establish the existence and uniqueness of a strong solution.
 1 12 107 . .
2008-01-07 2007-07-05 346 yes 1530 no 295 1 2008 5 0 Multiplicity of solutions for a class of quasilinear elliptic equations with concave and convex terms in R
In this paper the Fountain theorem is employed to establish infinitely many solutions for the class of quasilinear Schr\"{o}dinger equations $-L_pu+ V(x)|u|^{p-2}u=\lambda|u|^{q-2}u+\mu |u|^{r-2}u$ in $\mathbb{R}$, where $L_pu=(|u'|^{p-2}u')'+ (|(u^2)'|^{p-2}(u^2)')'u$, $\lambda, \mu$ are real parameters, $1 < p < \infty$, $1<q<p$, $r>2p$ and the potential $V(x)$ is nonnegative and satisfies a suitable integrability condition.
 1 16 20 . .
2008-02-04 2007-11-27 348 yes 296 1 2008 6 0 Oscillation and global asymptotic stability of a neuronic equation with two delays
In this paper we study the oscillatory and global asymptotic stability of a single neuron model with two delays and a general activation function. New sufficient conditions for the oscillation and nonoscillation of the model are given. We obtain both delay-dependent and delay-independent global asymptotic stability criteria. Some of our results are new even for models with one delay.
 1 21 25 . .
2008-02-04 2007-05-09 349 yes 350 no 297 1 2008 7 0 Positive solutions for nonlinear semipositone nth-order boundary value problems
In this paper, we investigate the existence of positive solutions for a class of nonlinear semipositone $n$th-order boundary value problems. Our approach relies on the Krasnosel'skii fixed point theorem. The result of this paper complement and extend previously known result.
 1 12 70 . .
2008-02-11 2007-10-30 352 yes 351 no 353 no 354 no 298 1 2008 8 0 Existence of positive solutions for nth-order boundary value problem with sign changing nonlinearity
In this paper, we investigate the existence of positive solutions for singular $n$th-order boundary value problem $u^{(n)}(t)+a(t)f(t,u(t))=0,\quad 0\le t\le1,$ $u^{(i)}(0)=u^{(n-2)}(1)=0,\quad 0\le i\le n-2,$ where $n\ge2$, $a\in C((0,1),[0,+\infty))$ may be singular at $t=0$ and (or) $t=1$ and the nonlinear term $f$ is continuous and is allowed to change sign. Our proofs are based on the method of lower solution and topology degree theorem.
 1 10 107 . .
2008-02-11 2007-08-17 352 yes 351 no 353 no 354 no 299 1 2008 9 0 An existence result for neutral functional differential inclusions in a Banach space
In this paper we prove the existence of mild solutions for semilinear neutral functional differential inclusions with unbounded linear part generating a noncompact semigroup in a Banach space. This work generalizes the result given in [4].
 1 23 70 . .
2008-03-15 2007-11-19 309 yes 355 no 300 1 2008 10 0 Local asymptotic stability for nonlinear quadratic functional integral equations
In the present study, using the characterizations of measures of noncompactness we prove a theorem on the existence and local asymptotic stability of solutions for a quadratic functional integral equation via a fixed point theorem of Darbo. The investigations are placed in the Banach space of real functions defined, continuous and bounded on an unbounded interval. An example is indicated to demonstrate the natural realizations of abstract result presented in the paper.
 1 13 107 . .
2008-03-15 2007-10-21 2747 yes 356 no 301 1 2008 11 0 On the oscillation of second order nonlinear neutral delay difference equations
In this paper sufficient conditions are obtained for oscillation of all solutions of a class of nonlinear neutral delay difference equations of the form $\Delta^2(y(n)+p(n)y(n-m))+q(n)G(y(n-k))=0$ under various ranges of $p(n)$. The nonlinear function $G, G \in C (R, R)$ is either sublinear or superlinear.
 1 12 7 . .
2008-03-15 2007-11-10 357 yes 302 1 2008 12 0 Qualitative properties of nonlinear Volterra integral equations
In this article, the contraction mapping principle and Liapunov's method are used to study qualitative properties of nonlinear Volterra equations of the form $x(t) = a(t) -\int^{t}_{0}C(t,s)g(s,x(s))\;ds,t\geq0.$ In particular, the existence of bounded solutions and solutions with various $L^p$ properties are studied under suitable conditions on the functions involved with this equation.
 1 16 857 . .
2008-03-15 2008-01-11 114 yes 1549 no 303 1 2008 13 0 On a parabolic strongly nonlinear problem on manifolds
In this work we will prove the existence uniqueness and asymptotic behavior of weak solutions for the system (*) involving the pseudo Laplacian operator and the condition $\displaystyle\frac{\partial u}{\partial t} + \sum_{i=1}^n \big|\frac{\partial u}{\partial x_i}\big|^{p-2}\frac{\partial u}{\partial x_i}\nu_i + |u|^{\rho}u=f$ on $\Sigma_1$, where $\Sigma_1$ is part of the lateral boundary of the cylinder $Q=\Omega \times (0,T)$ and $f$ is a given function defined on $\Sigma_1$.
 1 20 857 . .
2008-03-15 2007-08-25 359 yes 360 no 361 no 304 1 2008 14 0 A third-order 3-point BVP. Applying Krasnosel'skii's theorem on the plane without a Green's function
Consider the three-point boundary value problem for the 3$^{rd}$ order differential equation:

\begin{equation*}\left\{ \begin{tabular}{l}
$x^{^{\prime \prime \prime }}(t)=\alpha \left( t\right) f(t,x(t),x^{\prime}\left( t\right) ,x^{\prime \prime }\left( t\right) ),\;\;\;0<t<1,$ \\
$x\left( 0\right) =x^{\prime }\left( \eta \right) =x^{\prime \prime }\left(1\right) =0,$
\end{tabular}\right.\end{equation*}

under positivity of the nonlinearity. Existence results for a positive and concave solution $x\left( t\right) ,\ 0\leq t\leq 1$ are given, for any $1/2<\eta <1.\ $ In addition, without any monotonicity assumption on the nonlinearity, we prove the existence of a sequence of such solutions with \begin{equation*} \lim_{n\rightarrow \infty }||x_{n}||=0. \end{equation*} Our principal tool is \emph{a very simple applications on a new cone of the plane} of the well-known Krasnosel'ski\u{\i}'s fixed point theorem. The main feature of this aproach is that, we do not use at all the associated Green's function, the necessary positivity of which yields the restriction $\eta \in \left( 1/2,1\right) $. Our method still guarantees that the solution we obtain is positive.
 1 15 11 . .
2008-04-02 2007-12-25 362 yes 363 no 305 1 2008 15 0 Exact solutions to some nonlinear PDEs, travelling profiles method
We suggest finding exact solutions of equation:

\begin{equation*}
\frac{\partial u}{\partial t}=(\frac{\partial ^{m}}{\partial x^{m}}u)^{p},
t\geq 0, x\in \mathbb{R}, m, p\in \mathbb{N}, p>1,
\end{equation*}

by a new method that we call the travelling profiles method. This method allows us to find several forms of exact solutions including the classical forms such as travelling-wave and self-similar solutions.
 1 7 107 . .
2008-04-03 2007-07-02 364 yes 306 1 2008 16 0 Stability of a monotonic solution of a non-autonomous multidimensional delay differential equation of arbitrary (fractional) order
We are concerned here with the existence of monotonic and uniformly asymptotically stable solution of an initial-value problem of non-autonomous delay differential equations of arbitrary (fractional) orders.
 1 9 857 . .
2008-04-25 2008-01-03 312 yes 365 no 307 1 2008 17 0 The freezing method for Volterra integral equations in a Banach space
The "freezing" method for ordinary differential equations is extended to the Volterra integral equations in a Banach space of the type $$ x(t)- \int_0^t K(t, t-s)x(s)ds =f(t)\;(t\geq 0),$$ where $K(t,s)$ is an operator valued function "slowly" varying in the first argument. Besides, sharp explicit stability conditions are derived.
 1 7 857 . .
2008-04-25 2008-02-14 366 yes 309 1 2008 18 0 Two positive solutions for a nonlinear four-point boundary value problem with a p-Laplacian operator
In this paper, we study the existence of positive solutions for a nonlinear four-point boundary value problem with a $p$-Laplacian operator. By using a three functionals fixed point theorem in a cone, the existence of double positive solutions for the nonlinear four-point boundary value problem with a $p$-Laplacian operator is obtained. This is different than previous results.
 1 10 7 . .
2008-04-25 2008-01-16 367 yes 368 no 369 no 310 1 2008 19 0 Oscillatory and asymptotic behaviour of a neutral differential equation with oscillating coefficients
In this paper, we obtain sufficient conditions so that every solution of
$$
\big(y(t)- \sum_{i=1}^n p_i(t) y(\delta_i(t))\big)'+\sum_{i=1}^m q_i(t) y(\sigma_i(t)) = f(t)
$$
oscillates or tends to zero as $t \to \infty$. Here the coefficients $p_i(t), q_i(t)$ and the forcing term $f(t)$ are allowed to oscillate; such oscillation condition in all coefficients is very rare in the literature. Furthermore, this paper provides an answer to the open problem 2.8.3 in [7, p. 57]. Suitable examples are included to illustrate our results.
 1 10 107 . .
2008-05-15 2008-02-11 370 yes 371 no 372 no 373 no 311 1 2008 20 0 Localized radial solutions for a nonlinear p-Laplacian equation in $R^N$
We establish the existence of radial solutions to the p-Laplacian equation $ \Delta_p u + f(u)=0 $ in $\mathbb {R^N}$, where $f$ behaves like $|u|^{q-1}u$ when $u$ is large and $f(u) < 0$ for small positive $u$. We show that for each nonnegative integer $n$, there is a localized solution $u$ which has exactly $n$ zeros.
 1 23 79 . .
2008-05-25 2007-08-10 374 yes 312 1 2008 21 0 Bounded and almost automorphic solutions of a Liénard equation with a singular nonlinearity
We study some properties of bounded and $C^{(1)}$-almost automorphic solutions of the following Li\'enard equation: $$x'' + f(x)x' + g(x) = p(t) $$, where $p : {\bf R} \longrightarrow {\bf R}$ is an almost automorphic function, $f$, $g : (a,b) \longrightarrow {\bf R}$ are continuous functions and $g$ is strictly decreasing.
 1 15 867 . .
2008-05-25 2008-02-03 376 yes 377 no 378 no 314 1 2008 22 0 Existence of solutions of nth order impulsive integro-differential equations in Banach spaces
In this paper, we prove the existence of solutions of initial value problems for nth order nonlinear impulsive integro-differential equations of mixed type on an infinite interval with an infinite number of impulsive times in Banach spaces. Our results are obtained by introducing a suitable measure of noncompactness.
 1 11 4 . .
2008-05-28 2008-04-09 379 yes 380 no 337 1 2008 23 0 Exponential stability of linear stochastic differential equations with bounded delay and the W-transform
We demonstrate how the method of auxiliary ('reference') equations, also known as N. V. Azbelev's W-transform method, can be used to derive efficient conditions for the exponential Lyapunov stability of linear delay equations driven by a vector-valued Wiener process. For the sake of convenience the W-method is briefly outlined in the paper, its justification is however omitted. The paper contains a general stability result, which is specified in the last section in the form of seven corollaries providing sufficient stability conditions for some important classes of It\^{o} equations with delay.
 1 14 14 . .
2008-07-20 2007-01-30 397 yes 69 no 338 1 2008 24 0 Triple positive solutions for a boundary value problem of nonlinear fractional differential equation
In this paper, we investigate the existence of three positive solutions for the nonlinear fractional boundary value problem

$D_{0+}^{\alpha} u(t) + a(t)f(t,u(t), u^{\prime \prime}(t))=0, \quad 0 < t < 1, \quad 3 < \alpha \leq 4,$

$u(0) = u^{\prime}(0) = u^{\prime \prime}(0)= u^{\prime \prime}(1)=0 $,

where $D_{0+}^{\alpha}$ is the standard Riemann-Liouville fractional derivative. The method involves applications of a new fixed-point theorem due to Bai and Ge. The interesting point lies in the fact that the nonlinear term is allowed to depend on the second order derivative $u^{\prime \prime}$.
 1 10 70 . .
2008-07-25 2008-04-13 351 yes 339 1 2008 25 0 Integrable and continuous solutions of a nonlinear quadratic integral equation
We are concerned here with a nonlinear quadratic integral equation of Volterra type. The existence of at least one $L_1-$ positive solution will be proved under the Carath\`{e}odory condition. Secondly we will make a link between Peano condition and Carath\`{e}odory condition to prove the existence of at least one positive continuous solution. Finally the existence of the maximal and minimal solutions will be proved.
 1 10 0 . .
See also an addendum to this paper: EJQTDE, No. 51. 2009.
 2008-08-10 2008-04-30 312 yes 398 no 340 1 2008 26 0 Existence of Psi-bounded solutions for linear difference equations on Z
In this paper, we give a necessary and sufficient condition for the existence of $\Psi -$ bounded solutions for the nonhomogeneous linear difference equation x(n + 1) = A(n)x(n) + f(n) on $\mathbb{Z}$. In addition, we give a result in connection with the asymptotic behavior of the $\Psi -$ bounded solutions of this equation.
 1 13 79 . .
2008-09-10 2008-06-05 1389 yes 342 1 2008 27 0 Existence of solutions to neutral differential equations with deviated argument
In this paper we shall study a neutral differential equation with deviated argument in an arbitrary Banach space $X.$ With the help of the analytic semigroups theory and fixed point method we establish the existence and uniqueness of solutions of the given problem. Finally, we give examples to illustrate the applications of the abstract results.
 1 12 70 . .
2008-09-10 2008-06-18 401 yes 346 no 341 1 2008 28 0 Three positive solutions for p-Laplacian functional dynamic equations on time scales
In this paper, existence criteria of three positive solutions to the followimg $p$-Laplacian functional dynamic equation on time scales

\[\left\{\begin{array}{l}
\left[ \Phi _p(u^{\bigtriangleup }(t))\right] ^{\bigtriangledown}+a(t)f(u(t),u(\mu (t)))=0,t\in \left(0,T\right),\\
u_0(t)=\varphi (t), t\in \left[ -r,0\right], u(0)-B_0(u^{\bigtriangleup }(\eta ))=0, u^{\bigtriangleup }(T)=0,
\end{array}\right.\]

are established by using the well-known Five Functionals Fixed Point Theorem.
 1 7 107 . .
2008-09-10 2008-06-09 400 yes 343 1 2008 29 0 On the stability of a fractional-order differential equation with nonlocal initial condition
The topic of fractional calculus (integration and differentiation of fractional-order), which concerns singular integral and integro-differential operators, is enjoying interest among mathematicians, physicists and engineers. In this work, we investigate initial value problem of fractional-order differential equation with nonlocal condition. The stability (and some other properties concerning the existence and uniqueness) of the solution will be proved.
 1 8 4 . .
2008-09-30 2008-02-07 312 yes 311 no 345 1 2008 30 0 The foam drainage equation with time- and space-fractional derivatives solved by the Adomian method
In this paper, by introducing the fractional derivative in the sense of Caputo, we apply the Adomian decomposition method for the foam drainage equation with time- and space-fractional derivative. As a result, numerical solutions are obtained in a form of rapidly convergent series with easily computable components.
 1 10 71 . .
2008-10-10 2008-05-30 402 yes 403 no 404 no 344 1 2008 31 0 First order impulsive differential inclusions with periodic conditions
In this paper, we present an impulsive version of Filippov's Theorem for the first-order nonresonance impulsive differential inclusion
$$
\begin{array}{rlll}
y'(t)-\lambda y(t) &\in& F(t,y(t)), &\hbox{ a.e. } \, t\in J\backslash
\{t_{1},\ldots,t_{m}\},\\
y(t^+_{k})-y(t^-_k)&=&I_{k}(y(t_{k}^{-})), &k=1,\ldots,m,\\
y(0)&=&y(b),
\end{array}
$$
where $J=[0,b]$ and $F: J \times \R^n\to{\cal P}(\R^n)$ is a set-valued map. The functions $I_k$ characterize the jump of the solutions at impulse points $t_k$ ($k=1,\ldots,m.$). Then the relaxed problem is considered and a Filippov-Wasewski result is obtained. We also consider periodic solutions of the first order impulsive differential inclusion
$$
\begin{array}{rlll}
y'(t) &\in& \varphi(t,y(t)), &\hbox{ a.e. } \, t\in J\backslash
\{t_{1},\ldots,t_{m}\},\\
y(t^+_{k})-y(t^-_k)&=&I_{k}(y(t_{k}^{-})), &k=1,\ldots,m,\\
y(0)&=&y(b),
\end{array}
$$
where $\varphi: J\times \R^n\to{\cal P}(\R^n)$ is a multi-valued map. The study of the above problems use an approach based on the topological degree combined with a Poincar\'e operator.
 1 40 70 . .
2008-10-15 2008-07-11 7 yes 172 no 346 1 2008 32 0 Sharp oscillation criteria for fourth order sub-half-linear and super-half-linear differential equations
This paper is concerned with the oscillatory behavior of the fourth-order nonlinear differential equation
$$
\bigl(p(t)|x^{\prime\prime}|^{\alpha-1}\,x^{\prime\prime}\bigr)^{\prime\prime}
+q(t)|x|^{\beta-1}x=0\,,\leqno{\rm(E)}
$$
where $\alpha>0$, $\beta>0$ are constants and $p,q:[a,\infty)\to(0,\infty)$ are continuous functions satisfying conditions
$$
\int_a^{\infty}\left( \frac{t}{p(t)}\right)^{\frac{1}{\alpha}}\,dt<\infty,
\int_a^{\infty}\frac{t}{\left(p(t)\right)^{\frac{1}{\alpha}}}\,dt<\infty .
$$
We will establish necessary and sufficient condition for oscillation of all solutions of the sub-half-linear equation (E) (for $\beta<\alpha$) as well as of the super-half-linear equation (E) (for $\beta>\alpha$).
 1 13 7 . .
2008-11-01 2008-07-26 1763 yes 405 no 348 1 2008 33 0 Multivalued evolution equations with infinite delay in Fréchet spaces
In this paper, sufficient conditions are given to investigate the existence of mild solutions on a semi-infinite interval for two classes of first order semilinear functional and neutral functional differential evolution inclusions with infinite delay using a recent nonlinear alternative for contractive multivalued maps in Fr\'echet spaces due to Frigon, combined with semigroup theory.
 1 24 857 . .
2008-11-01 2008-07-05 408 yes 71 no 347 1 2008 34 0 Existence and boundary stabilization of the semilinear Mindlin-Timoshenko system
We consider dynamics of the one-dimensional Mindlin-Timoshenko model for beams with a nonlinear external forces and a boundary damping mechanism. We investigate existence and uniqueness of strong and weak solution. We also study the boundary stabilization of the solution, i.e., we prove that the energy of every solution decays exponentially as $t\rightarrow\infty$.
 1 27 79 . .
2008-11-01 2008-04-17 406 yes 407 no 349 1 2008 35 0 Existence of $S^2$-almost periodic solutions to a class of nonautonomous stochastic evolution equations
The paper studies the notion of Stepanov almost periodicity (or $S^2$-almost periodicity) for stochastic processes, which is weaker than the notion of quadratic-mean almost periodicity. Next, we make extensive use of the so-called Acquistapace and Terreni conditions to prove the existence and uniqueness of a Stepanov (quadratic-mean) almost periodic solution to a class of nonautonomous stochastic evolution equations on a separable real Hilbert space. Our abstract results will then be applied to study Stepanov (quadratic-mean) almost periodic solutions to a class of $n$-dimensional stochastic parabolic partial differential equations.
 1 19 70 . .
2008-11-05 2008-08-10 409 yes 947 no 352 1 2008 36 0 Forced oscillation of second order nonlinear dynamic equations on time scales
By means of the Kartsatos technique and generalized Riccati transformation techniques, we establish some new oscillation criteria for a second order nonlinear dynamic equations with forced term on time scales in terms of the coefficients.
 1 13 71 . .
2008-11-15 2006-10-10 411 yes 412 no 350 1 2008 37 0 Mixed semicontinuous perturbation of a second order nonconvex sweeping process
We prove a theorem on the existence of solutions of a second order differential inclusion governed by a class of nonconvex sweeping process with a mixed semicontinuous perturbation.
 1 9 107 . .
2008-11-15 2008-06-29 410 yes 351 1 2008 38 0 Radial solutions to a superlinear Dirichlet problem using Bessel functions
We look for radial solutions of a superlinear problem in a ball. We show that for if $n$ is a sufficiently large nonnegative integer, then there is a solution $u$ which has exactly $n$ interior zeros. In this paper we give an alternate proof to that which was given by Castro and Kurepa.
 1 13 79 . .
2008-11-15 2008-08-08 130 yes 374 no 354 1 2009 1 0 Growth of meromorphic solutions of higher-order linear differential equations
In this paper, we investigate the higher-order linear differential equations with meromorphic coefficients. We improve and extend a result of M.S. Liu and C.L. Yuan, by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen, and the extended Winman-Valiron theory which proved by J. Wang and H.X. Yi. In addition, we also consider the nonhomogeneous linear differential equations.
 1 13 107 . .
2009-01-08 2008-08-06 416 yes 415 no 355 1 2009 2 0 The generalized approximation method and nonlinear heat transfer equations
Generalized approximation technique for a solution of one-dimensional steady state heat transfer problem in a slab made of a material with temperature dependent thermal conductivity, is developed. The results obtained by the generalized approximation method (GAM) are compared with those studied via homotopy perturbation method (HPM). For this problem, the results obtained by the GAM are more accurate as compared to the HPM. Moreover, our (GAM) generate a sequence of solutions of linear problems that converges monotonically and rapidly to a solution of the original nonlinear problem. Each approximate solution is obtained as the solution of a linear problem. We present numerical simulations to illustrate and confirm the theoretical results.
 1 15 107 . .
2009-01-10 2008-08-17 221 yes 356 1 2009 3 0 New results on the positive solutions of nonlinear second-order differential systems
In this paper, we study the three-point boundary value problems for systems of nonlinear second order ordinary differential equations of the form
$$
\left\{\aligned &u''=-f(t,v), \ \ 0< t< 1,\\&v''=-g(t,u), \ \ 0< t< 1\\&u(0)=v(0)=0,\varsigma u(\zeta)=u(1),\varsigma v(\zeta)=v(1),\endaligned\right.
$$
where $f:(0,1)\times [0,+\infty)\to [0,+\infty),g:[0,1]\times [0,+\infty)\to [0,+\infty),0<\zeta<1, \varsigma>0,$ and $\varsigma\zeta< 1,f$ may be singular at $t = 0$ and/or $t = 1.$ Under some rather simple conditions, by means of monotone iterative technique, a necessary and sufficient condition for the existence of positive solutions is established, a result on the existence and uniqueness of the positive solution and the iterative sequence of solution is given.
 1 16 70 . .
2009-01-15 2008-07-29 1177 yes 357 1 2009 4 0 Periodic solutions of a class of integrodifferential impulsive periodic systems with time-varying generating operators on Banach space
This paper deals with a class of integrodifferential impulsive periodic systems with time-varying generating operators on Banach space. Using impulsive periodic evolution operator given by us, the suitable $T_{0}$-periodic $PC$-mild solution is introduced and $Poincar\acute{e}$ operator is constructed. Showing the compactness of $Poincar\acute{e}$ operator and using a new generalized Gronwall's inequality with impulse, mixed type integral operators and $B$-norm given by us, we utilize Leray-Schauder fixed point theorem to prove the existence of $T_{0}$-periodic $PC$-mild solutions. Our method is much different from methods of other papers. At last, an example is given for demonstration.
 1 17 7 . .
2009-01-15 2008-10-04 418 yes 419 no 420 no 358 1 2009 5 0 Positive solutions of second order semipositone singular three-point boundary value problems
In this paper we prove the existence of positive solutions for a class of second order semipositone singular three-point boundary value problems. The results are obtained by the use of a Guo-Krasnoselskii's fixed point theorem in cones.
 1 11 70 . .
2009-01-28 2008-09-10 1177 yes 359 1 2009 6 0 Existence of solutions for a certain differential inclusion of third order
The existence of solutions of a boundary value problem for a third order differential inclusion is investigated. New results are obtained by using suitable fixed point theorems when the right hand side has convex or non convex values.
 1 9 70 . .
2009-02-10 2008-10-07 317 yes 360 1 2009 7 0 Monotonic solutions of functional integral and differential equations of fractional order
The existence of positive monotonic solutions, in the class of continuous functions, for some nonlinear quadratic integral equations have been studied by J. Banas. Here we are concerned with a singular quadratic functional integral equations. The existence of positive monotonic solutions $x \in L_1[0,1]$ will be proved. The fractional order nonlinear functional differential equation will be given as a special case.
 1 8 857 . .
2009-02-15 2008-06-18 312 yes 398 no 361 1 2009 8 0 Stability in discrete equations with variable delays
In this paper we study the stability of the zero solution of difference equations with variable delays. In particular we consider the scalar delay equation
\begin{equation}
\Delta x(n)=-a(n)x(n-\tau(n))
\end{equation}
and its generalization
\begin{equation}
\Delta x(n)=-\sum^{N}_{j=1}a_j(n)x(n-\tau_j(n)).
\end{equation}
Fixed point theorems are used in the analysis.
 1 7 107 . .
2009-02-16 2008-11-14 288 yes 362 1 2009 9 0 Multiple positive solutions for nonlinear third order general two-point boundary value problems
We consider the existence of positive solutions and multiple positive solutions for the third order nonlinear differential equation subject to the general two-point boundary conditions using different fixed point theorems.
 1 17 107 . .
2009-02-20 2008-11-14 422 yes 423 no 363 1 2009 10 0 Bounded weak solutions to nonlinear elliptic equations
In this work, we are concerned with a class of elliptic problems with both absorption terms and critical growth in the gradient. We suppose that the data belong to $L^{m}(\Omega)$ with $m>n/2$ and we prove the existence of bounded weak solutions via $L^{\infty}$-estimates. A priori estimates and Stampacchia's $L^{\infty}$-regularity are our main ingredient.
 1 16 20 . .
2009-03-12 2008-11-17 148 yes 424 no 364 1 2009 11 0 On the solvability of anti-periodic boundary value problems with impulses
In this paper, we are concerned with the existence of solutions for second order impulsive anti-periodic boundary value problem
${ \left \{\begin{array} {l}
u''(t) + f(t,u(t),u'(t))=0, \quad t \not= t_k, \ t \in [0, T], \\
\triangle u(t_k) = I_k(u(t_k)), \quad k = 1, \cdots , m, \\
\triangle u'(t_k) = I_k^*(u(t_k)), \quad k = 1, \cdots , m, \\
u(0) + u(T) = 0, \ u'(0) + u'(T) = 0.
\end{array}\right.} $
New criteria are established based on Schaefer's fixed-point theorem.
 1 15 70 . .
2009-03-16 2008-12-16 351 yes 365 1 2009 12 0 Discretization methods for nonconvex differential inclusions
We prove the existence of solutions for the differential inclusion $\dot x(t)\in F(t,x(t)) + f(t,x(t))$ for a multifunction $F$ upper semicontinuous with compact values contained in the generalized Clarke gradient of a regular locally Lipschitz function and $f$ a Carath\'{e}odory function.
 1 10 71 . .
2009-03-16 2008-06-27 421 yes 366 1 2009 13 0 A note on a nonlinear functional differential system with feedback control
In this note we apply Avery-Peterson multiple fixed point theorem to investigate the existence of multiple positive periodic solutions to the following nonlinear non-autonomous functional differential system with feedback control
\[\left\{\begin{array}{l}
\frac{dx}{dt}=-r(t)x(t)+F(t,x_t,u(t-\delta(t))),\\
\frac{du}{dt}=-h(t)u(t)+g(t)x(t-\sigma(t)).\\
\end{array}\right.\]
We prove the system above admits at least three positive periodic solutions under certain growth conditions imposed on $F$.
 1 9 70 . .
2009-03-21 2008-12-15 425 yes 426 no 367 1 2009 14 0 Three positive solutions to initial-boundary value problems of nonlinear delay differential equations
In this paper, we consider the existence of triple positive solutions to the boundary value problem of nonlinear delay differential equation
$$
\left\{ \begin{array}{lll}
(\phi(x'(t)))^{\prime} + a(t)f(t,x(t),x'(t),x_{t})=0, \ \ 0 < t<1,\\
x_{0}=0,\\
x(1)=0,
\end{array}\right.
$$
where $\phi: \R \rightarrow \R$ is an increasing homeomorphism and positive homomorphism with $\phi(0)=0,$ and $x_t$ is a function in $C([-\tau,0],\R)$ defined by $x_{t}(\sigma)=x(t+\sigma)$ for $ -\tau \leq \sigma\leq 0.$ By using a fixed-point theorem in a cone introduced by Avery and Peterson, we provide sufficient conditions for the existence of triple positive solutions to the above boundary value problem. An example is also presented to demonstrate our result. The conclusions in this paper essentially extend and improve the known results.
 1 11 7 . .
2009-03-21 2008-11-21 427 yes 428 no 368 1 2009 15 0 Strongly nonlinear problem of infinite order with $L^1$ data
In this paper, we prove the existence of solutions for the strongly nonlinear equation of the type $$ Au+g(x,u)=f $$ where $A$ is an elliptic operator of infinite order from a functional space of Sobolev type to its dual. $g(x,s)$ is a lower order term satisfying essentially a sign condition on $s$ and the second term $f$ belongs to $L^1(\Omega).$
 1 12 24 . .
2009-03-21 2008-03-11 179 yes 429 no 430 no 369 1 2009 16 0 Asymptotic and oscillatory behavior of second order neutral quantum equations with maxima
In this study, the behavior of solutions to certain second order quantum ($q$-difference) equations with maxima are considered. In particular, the asymptotic behavior of non-oscillatory solutions is described, and sufficient conditions for oscillation of all solutions are obtained.
 1 9 107 . .
2009-03-21 2009-01-19 322 yes 431 no 370 1 2009 17 0 $Psi-$ bounded solutions for a Lyapunov matrix differential equation
It is proved a necessary and sufficient condition for the existence of at least one $Psi-$bounded solution of a linear nonhomogeneous Lyapunov matrix differential equation.
 1 11 79 . .
2009-03-21 2008-11-12 1389 yes 372 1 2009 18 0 A generalized Fucik type eigenvalue problem for p-Laplacian
In this paper we study the generalized Fucik type eigenvalue for the boundary value problem of one dimensional $p-$Laplace type differential equations
\begin{displaymath}\left\{
\begin{array}{lll} - (\varphi( u')) ' = \psi(u), \quad -T< x < T; \\
\quad u(-T)=0, \quad u(T)=0 \\
\end{array} \right.\eqno(*)
\end{displaymath}
where $\varphi (s) = \alpha s_+^{p-1} -\beta s_-^{p-1}, \psi (s) = \lambda s_+^{p-1} -\mu s_-^{p-1}, p >1.$ We obtain a explicit characterization of Fucik spectrum $(\alpha, \beta, \lambda, \mu),$ i.e., for which the (*) has a nontrivial solution.
 1 9 857 . .
2009-03-21 2008-01-15 434 yes 371 1 2009 19 0 Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a half-line
This paper investigates the solvability of the second-order boundary value problems with the one-dimensional $p$-Laplacian at resonance on a half-line
$$
\left\{\begin{array}{llll}
(c(t)\phi_{p}(x'(t)))'=f(t,x(t),x'(t)),~~~~0<t<\infty,\\
x(0)=\sum\limits_{i=1}\limits^{n}\mu_ix(\xi_{i}),
~~\lim\limits_{t\rightarrow +\infty}c(t)\phi_{p}(x'(t))=0
\end{array}\right.
$$
and
$$\left\{\begin{array}{llll}
(c(t)\phi_{p}(x'(t)))'+g(t)h(t,x(t),x'(t))=0,~~~~0<t<\infty,\\
x(0)=\int_{0}^{\infty}g(s)x(s)ds,~~\lim\limits_{t\rightarrow
+\infty}c(t)\phi_{p}(x'(t))=0
\end{array}\right.
$$
with multi-point and integral boundary conditions, respectively, where $\phi_{p}(s)=|s|^{p-2}s$, $p>1$. The arguments are based upon an extension of Mawhin's continuation theorem due to Ge. And examples are given to illustrate our results.
 1 15 7 . .
2009-03-23 2008-06-12 433 yes 2135 no 300 no 374 1 2009 20 0 Solutions to a class of nonlinear differential equations of fractional order
In this paper we investigate the formulation of a class of boundary value problems of fractional order with the Riemann-Liouville fractional derivative and integral-type boundary conditions. The existence of solutions is established by applying a fixed point theorem of Krasnosel'skii and Zabreiko for asymptotically linear mappings.
 1 10 107 . .
2009-04-13 2009-02-25 237 yes 373 1 2009 21 0 Periodic boundary value problems of second order random differential equations
In this paper, an existence and the existence of extremal random solutions are proved for a periodic boundary value problem of second order ordinary random differential equations. Our investigations have been placed in the space of real-valued functions defined and continuous on closed and bounded intervals of real line together with the applications of the random version of a nonlinear alternative of Leray-Schauder type and an algebraic random fixed point theorem of Dhage. An example is also indicated for demonstrating the realizations of the abstract theory developed in this paper.
 1 14 71 . .
2009-04-13 2009-01-23 2747 yes 435 no 70 no 375 1 2009 22 0 On oscillation theorems for differential polynomials
In this paper, we investigate the relationship between small functions and differential polynomials $g_{f}\left( z\right)=d_{2}f^{^{\prime \prime }} + d_{1}f^{^{\prime }}+d_{0}f$, where $d_{0}\left(z\right), d_{1}\left( z\right), d_{2}\left( z\right) $ are meromorphic functions that are not all equal to zero with finite order generated by solutions of the second order linear differential equation
\begin{equation*}
f^{^{\prime \prime }}+Af^{^{\prime }}+Bf=F,
\end{equation*}
where $A,$ $B,$ $F\not\equiv 0$ are finite order meromorphic functions having only finitely many poles.
 1 10 107 . .
2009-04-13 2008-12-31 436 yes 1377 no 376 1 2009 23 0 Criteria for disfocality and disconjugacy for third order differential equations
In this paper, lower bounds for the spacing $(b - a)$ of the zeros of the solutions and the zeros of the derivative of the solutions of third order differential equations of the form \[y''' + q(t) y' + p(t)y = 0 (*)\] are derived under the some assumptions on $p$ and $q$. The concept of disfocality is introduced for third order differential equations (*). This helps to improve the Liapunov-type inequality, when y(t) is a solution of (*) with (i) $ y(a) = 0 = y'(b)$ or $ y'(a) = 0 = y(b) $ with $ y(t) \ne 0, t \in (a,b) $ or (ii) $ y(a) = 0 = y'(a), y(b) = 0 = y'(b)$ with $ y(t)\ne 0, t\in (a,b)$. If y(t) is a solution of (*) with $ y(t_{i}) = 0, 1 \le i \le n, n\ge 4, (t_{1} <t_{2} < ...< t_{n} )$ and $ y(t) \neq 0, t \in \bigcup_{i = 1}^{i =n - 1} (t_{i}, t_{i+1})$, then lower bound for spacing $(t_{n}-t_{1})$ is obtained. A new criteria for disconjugacy is obtained for (*) in $[a,b]$.This papers improves many known bounds in the literature.
 1 17 7 . .
2009-04-13 2008-11-01 900 yes 377 1 2009 24 0 Structure of solutions sets and a continuous version of Filippov's theorem for first order impulsive differential inclusions with periodic conditions
In this paper, the authors consider the first-order nonresonance impulsive differential inclusion with periodic conditions
$$
\begin{array}{rlll}
y'(t)-\lambda y(t) &\in& F(t,y(t)), &\hbox{ a.e. } \, t\in
J\backslash \{t_{1},\ldots,t_{m}\},\\
y(t^+_{k})-y(t^-_k)&=&I_{k}(y(t_{k}^{-})), &k=1, 2, \ldots,m,\\
y(0)&=&y(b),
\end{array}
$$
where $J=[0,b]$ and $F: J\times \R^n\to{\cal P}(\R^n)$ is a set-valued map. The functions $I_k$ characterize the jump of the solutions at impulse points $t_k$ ($k=1, 2, \ldots,m$). The topological structure of solution sets as well as some of their geometric properties (contractibility and $R_\delta$-sets) are studied. A continuous version of Filippov's theorem is also proved.
 1 23 70 . .
2009-04-20 2009-02-20 7 yes 172 no 378 1 2009 25 0 A Problem on the zeros of the Mittag-Leffler function and the spectrum of a fractional-order differential operator
We carry out spectral analysis of one class of integral operators associated with fractional order differential equations that arises in mechanics. We establish a connection between the eigenvalues of these operators and the zeros of Mittag-Leffler type functions. We give sufficient conditions for complete nonselfadjointness and completeness the systems of the eigenvalues.
 1 18 11 . .
2009-04-27 2008-01-31 438 yes 439 no 379 1 2009 26 0 Existence results for impulsive neutral functional differential equations with state-dependent delay
In this article, we study the existence of mild solutions for a class of impulsive abstract partial neutral functional differential equations with state-dependent delay. The results are obtained by using Leray-Schauder Alternative fixed point theorem. Example is provided to illustrate the main result.
 1 13 7 . .
2009-04-28 2008-11-19 440 yes 441 no 380 1 2009 27 0 Absence of nontrivial solutions for a class of partial differential equations and systems in unbounded domains
In this paper, we are interested in the study of the nonexistence of nontrivial solutions for a class of partial differential equations, in unbounded domains. This leads us to extend these results to systems of m equations. The method used is based on energy type identities.
 1 10 20 . .
2009-04-28 2009-01-06 442 yes 1314 no 381 1 2009 28 0 Some existence results for boundary value problems of fractional semilinear evolution equations
In this paper, we study the existence of solutions for a two-point boundary value problem of fractional semilinear evolution equations in a Banach space. Our results are based on the contraction mapping principle and Krasnoselskii's fixed point theorem.
 1 7 7 . .
2009-04-30 2009-03-19 307 yes 382 1 2009 29 0 Existence results for abstract partial neutral integro-differential equation with unbounded delay
In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.
 1 23 70 . .
2009-04-30 2009-02-21 444 yes 445 no 446 no 383 1 2009 30 0 Upper and lower solutions method and a fractional differential equation boundary value problem
The method of lower and upper solutions for fractional differential equation $D^\delta u(t)+g(t,u(t))=0, t\in (0,1), 1<\delta\leq 2$, with Dirichlet boundary condition $u(0)=a, u(1)=b$ is used to give sufficient conditions for the existence of at least one solution.
1 13 0 . . 2009-05-15 2009-01-24 447 yes 1396 no 384 1 2009 31 0 Positive solutions of boundary value problems for systems of second-order differential equations with integral boundary condition on the half-line
In this paper, we study the existence of positive solutions of boundary value problems for systems of second-order differential equations with integral boundary condition on the half-line. By using the fixed-point theorem in cones, we show the existence of at least one positive solution with suitable growth conditions imposed on the nonlinear terms. Moreover, the associated integral kernels for the boundary value problems are given.
 1 13 414 . .
2009-05-15 2009-03-23 449 yes 450 no 451 no 385 1 2009 32 0 Multiple positive solutions for the system of higher order two-point boundary value problems on time scales
In this paper, we establish the existence of at least three positive solutions for the system of higher order boundary value problems on time scales by using the well-known Leggett-Williams fixed point theorem. And then, we prove the existence of at least 2k-1 positive solutions for arbitrary positive integer k.
 1 13 107 . .
2009-05-15 2009-03-14 422 yes 452 no 453 no 386 1 2009 33 0 Multiple global bifurcation branches for nonlinear Picard problems
In this paper we prove the global bifurcation theorem for the nonlinear Picard problem. The right-hand side function $\varphi$ is a Caratheodory map, not differentiable at zero, but behaving in the neighbourhood of zero as specified in details below. We prove that in some interval $[a,b]\subset\real$ the Leray\--Schauder degree changes, hence there exists the global bifurcation branch. Later, by means of some approximation techniques, we prove that there exist at least two such branches.
 1 15 79 . .
2009-05-15 2008-12-16 454 yes 387 1 2009 34 0 Unbounded oscillation of higher-order nonlinear delay dynamic equations of neutral type with oscillating coefficients
In this paper, we present a criterion on the oscillation of unbounded solutions for higher-order dynamic equations of the following form:
\begin{equation}
\big[x(t)+A(t)x(\alpha(t))\big]^{\Delta^{n}}+B(t)F(x(\beta(t)))=\varphi(t)\qquad\text{for}\ t\in[t_{0},\infty)_{\T},\label{asbeq1}\tag{$\star$}
\end{equation}
where $n\in[2,\infty)_{\Z}$, $t_{0}\in\T$, $\sup\{\T\}=\infty$, $A\in\crd([t_{0},\infty)_{\T},\R)$ is allowed to alternate in sign infinitely many times, $B\in\crd([t_{0},\infty)_{\T},\R^{+})$, $F\in\crd(\R,\R)$ is nondecreasing, and $\alpha,\beta\in\crd([t_{0},\infty)_{\T},\T)$ are unbounded increasing functions satisfying $\alpha(t),\beta(t)\leq t$ for all sufficiently large $t$. We give change of order formula for double(iterated) integrals to prove our main result. Some simple examples are given to illustrate the applicability of our results too. In the literature, almost all of the results for \eqref{asbeq1} with $\T=\R$ and $\T=\Z$ hold for bounded solutions. Our results are new and not stated in the literature even for the particular cases $\T=\R$ and/or $\T=\Z$.
 1 14 7 . .
2009-05-25 2008-08-30 455 yes 388 1 2009 35 0 Triple positive solutions for second-order four-point boundary value problem with sign changing nonlinearities
In this paper, we study the existence of triple positive solutions for second-order four-point boundary value problem with sign changing nonlinearities. We first study the associated Green's function and obtain some useful properties. Our main tool is the fixed point theorem due to Avery and Peterson. The results of this paper are new and extent previously known results.
 1 14 70 . .
2009-06-02 2009-02-25 352 yes 353 no 351 no 389 1 2009 36 0 On a non-local boundary value problem for linear functional differential equations
We establish new efficient conditions for the unique solvability of a non-local boundary value problem for first-order linear functional differential equations. Differential equations with argument deviations are also considered in which case further results are obtained. The results obtained reduce to those well-known for the ordinary differential equations.
 1 13 11 . .
2009-06-05 2009-04-24 250 yes 456 no 390 1 2009 37 0 Boundedness and exponential stability for periodic time dependent systems
The time dependent $2$-periodic system
\begin{equation*}
\dot x{(t)} = A(t)x{(t)} , \ t\in \mathbb{R}, \ \ x(t) \in\mathbb{C}^{n}\eqno{(A(t))}
\end{equation*}
is uniformly exponentially stable if and only if for each real number $\mu$ and each $2$-periodic, $\mathbb{C}^{n}$-valued function $f,$ the solution of the Cauchy Problem
\begin{equation*}
\left\{\begin{split}
\dot y{(t)} &= A(t) y{(t)} + e^{i \mu t}f(t),\ \ t\in \mathbb{R}_+, \ y(t) \in \mathbb{C}^{n} \\
y(0) &= 0
\end{split}\right.
\end{equation*}
is bounded. In this note we prove a result that has the above result as an immediate corollary. Some new characterizations for uniform exponential stability of $(A(t))$ in terms of the Datko type theorems are also obtained as corollaries.
 1 9 71 . .
2009-06-10 2009-02-14 901 yes 457 no 392 1 2009 38 0 Green's function and positive solutions of a singular nth-order three-point boundary value problem on time scales
In this paper, we investigate the existence of positive solutions for a class of singular $n$th-order three-point boundary value problem. The associated Green's function for the boundary value problem is given at first, and some useful properties of the Green's function are obtained. The main tool is fixed-point index theory. The results obtained in this paper essentially improve and generalize some well-known results.
 1 14 107 . .
2009-06-15 2008-10-26 352 yes 353 no 351 no 391 1 2009 39 0 On the strongly damped wave equation with nonlinear damping and source terms
We consider a wave equation in a bounded domain with nonlinear dissipation and nonlinear source term. Characterizations with respect to qualitative properties of the solution: globality, boundedness, blow-up, convergence up to a subsequence towards the equilibria and exponential stability are given in this article.
 1 18 14 . .
2009-06-20 2009-01-06 458 yes 393 1 2009 40 0 Positive solutions for a multi-point eigenvalue problem involving the one dimensional $p$-Laplacian
A multi-point boundary value problem involving the one dimensional $p$-Laplacian and depending on a parameter is studied in this paper and existence of positive solutions is established by means of a fixed point theorem for operators defined on Banach spaces with cones.
 1 13 7 . .
2009-06-25 2009-02-14 460 yes 300 no 1232 no 394 1 2009 41 0 Solvability for second order nonlinear impulsive boundary value problems
In this paper, we are concerned with the solvability for a class of second order nonlinear impulsive boundary value problem. New criteria are established based on Schaefer's fixed-point theorem. An example is presented to illustrate our main result. Our results essentially extend and complement some previous known results.
 1 11 107 . .
2009-06-25 2009-02-17 462 yes 463 no 395 1 2009 42 0 Positive solutions of singular four-point boundary value problem with $p$-Laplacian
In this paper, we deal with the following singular four-point boundary value problem with $p$-Laplacian
$$
\left\{\begin{aligned}
&(\phi_{p}(u'(t)))'+q(t)f(t,u(t))=0,\ t\in(0,1),\\
&u(0)-\alpha u'(\xi)=0,\ u(1)+\beta u'(\eta)=0,
\end{aligned}\right.
$$
where $f(t,u)$ may be singular at $u=0$ and $q(t)$ may be singular at $t=0$ or $1$. By imposing some suitable conditions on the nonlinear term $f$, existence results of at least two positive solutions are obtained. The proof is based upon theory of Leray-Schauder degree and Krasnosel'skii's fixed point theorem.
 1 16 70 . .
2009-06-25 2009-03-03 2135 yes 464 no 300 no 396 1 2009 43 0 Positive solutions for singular m-point boundary value problems with sign changing nonlinearities depending on $x'$
Using the theory of fixed point theorem in cone, this paper presents the existence of positive solutions for the singular $m$-point boundary value problem
$$
\left\{\begin{array}{ll}
x''(t)+a(t)f(t,x(t),x'(t))=0,0<t<1,\\
x'(0)=0,\ \ x(1)=\dis \sum_{i=1}^{m-2}\alpha_{i}x(\xi_{i}),
\end{array}\right.
$$
where $0<\xi_{1}<\xi_{2}<\cdots<\xi_{m-2}<1, \alpha_{i}\in [0,1)$, $i = 1, 2, \cdots m-2$ , with $0<\sum_{i=1}^{m-2}\alpha_{i}<1$ and $f$ may change sign and may be singular at $x=0$ and $x'=0$.
 1 14 107 . .
2009-06-27 2008-09-19 465 yes 466 no 397 1 2009 44 0 Some results of nontrivial solutions for a nonlinear PDE in Sobolev space
In this study, we investigate the question of nonexistence of nontrivial solutions of the Robin problem
\begin{equation}
\left\vert\begin{array}{l}
-\dfrac{\partial ^{2}u}{\partial x^{2}}-\sum\limits_{s=1}^{n}\dfrac{\partial}{\partial y_{s}}a_{s}(y,\frac{\partial u}{\partial y_{s}})+f(y,u)=0\text{in }\Omega =\mathbb{R}\times D, \\ \\
u+\varepsilon \dfrac{\partial u}{\partial n}=0\text{ on }\mathbb{R}\times \partial D.
\end{array}\right. \tag*{$\left( P\right) $}
\end{equation}
where $a_{s}:D\times \mathbb{R}\rightarrow \mathbb{R}$ are $H^{1}$-functions with constant sign such that
\begin{equation}\begin{array}{c}
2\int\limits_{0}^{\xi _{s}}a_{s}(y,t_{s})dt_{s}-\xi _{s}a_{s}(y,\xi_{s})\leq 0,s=1,...,n
\end{array}\tag*{$\left( H_{1}\right) $}\end{equation}
and $f:D\times \mathbb{R}\rightarrow \mathbb{R}$ is a real continuous locally Liptschitz function such that
\begin{equation} 2F(y,u)-uf(y,u)\leq 0, \tag*{$\left( H_{2}\right) $} \end{equation}.
We show that the function \begin{equation*} E(x)=\int\limits_{D}\left\vert u(x,y)\right\vert ^{2}dy \end{equation*} is convex on $\mathbb{R}$ . Our proof is based on energy (integral) identities.
1 14 20 . .
2009-07-11 2009-06-01 467 yes 1314 no 398 1 2009 45 0 The constructive approach on existence of time optimal controls of system governed by nonlinear equations on Banach spaces
In this paper, a new approach to the existence of time optimal controls of system governed by nonlinear equations on Banach spaces is provided. A sequence of Meyer problems is constructed to approach a class of time optimal control problems. A deep relationship between time optimal control problems and Meyer problems is presented. The method is much different from standard methods.
 1 10 25 . .
2009-07-20 2009-01-13 418 yes 419 no 420 no 399 1 2009 46 0 Bounded and periodic solutions of nonlinear integro-differential equations with infinite delay
By using the concept of integrable dichotomy, the fixed point theory, functional analysis methods and some new technique of analysis, we obtain new criteria for the existence and uniqueness of bounded and periodic solutions of general and periodic systems of nonlinear integro-differential equations with infinite delay.
 1 20 857 . .
2009-07-20 2008-10-14 468 yes 400 1 2009 47 0 Existence of solutions for semilinear differential equations with nonlocal conditions in Banach spaces
This paper is concerned with semilinear differential equations with nonlocal conditions in Banach spaces. Using the tools involving the measure of noncompactness and fixed point theory, existence of mild solutions is obtained without the assumption of compactness or equicontinuity on the associated linear semigroup.
 1 13 70 . .
2009-07-23 2009-04-12 469 yes 463 no 401 1 2009 48 0 Fixed points of the derivative and k-th power of solutions of complex linear differential equations in the unit disc
In this paper we consider the question of the existence of fixed points of the derivatives of solutions of complex linear differential equations in the unit disc. This work improves some very recent results of T.-B. Cao.
 1 9 107 . .
2009-07-27 2009-02-26 471 yes 470 no 435 1 2009 49 0 Global existence and blow-up analysis for some degenerate and quasilinear parabolic systems
This paper deals with positive solutions of some degenerate and quasilinear parabolic systems not in divergence form: $u_{1t}=f_1(u_2)(\Delta u_1+a_1u_1),\cdots, u_{(n-1)t}=f_{n-1}(u_n)(\Delta u_{n-1}+a_{n-1} u_{n-1}),\ u_{nt}=f_n(u_1)(\Delta u_n+a_nu_n)$ with homogeneous Dirichlet boundary condition and positive initial condition, where $a_i\ (i=1,2,\cdots,n)$ are positive constants and $f_i\(i=1,2,\cdots,n)$ satisfy some conditions. The local existence and uniqueness of classical solution are proved. Moreover, it will be proved that: (i) when $\min\{a_1,\cdots,\ a_n\}\leq\lambda_1$ then there exists global positive classical solution, and all positive classical solutions can not blow up in finite time in the meaning of maximum norm; (ii) when $\min\{a_1,\cdots,\ a_n\}>\lambda_1$, and the initial datum $(u_{10},\cdots,\ u_{n0})$ satisfies some assumptions, then the positive classical solution is unique and blows up in finite time, where $\lambda_1$ is the first eigenvalue of $-\Delta$ in $\Omega$ with homogeneous Dirichlet boundary condition.
 1 14 7 . .
2009-08-20 2009-06-08 509 yes 436 1 2009 50 0 Global solutions for abstract functional differential equations with nonlocal conditions
In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered.
 1 8 70 . .
2009-08-24 2009-05-05 444 yes 510 no 437 1 2009 51 0 Addendum to integrable and continuous solutions of a nonlinear quadratic integral equation
This addendum concerns the paper of the above title found in EJQTDE No. 25 (2008). There are some misprints in that paper:

(i) Page 3, line 5 should be $k:[0,1] \times[0,1]\rightarrow R_+$ satisfies Carath\'{e}odory condition (i.e. measurable in $t$ for all $s \in [0,1]$ and continuous in $s$ for all $t\in [0,1]$) such that $\int_0^1 k(t,s) m_2(s)ds$ is bounded $\forall t\in[0,1].$

(ii) Page 6, line 6 should be $k:[0,1] \times [0,1]\rightarrow R_+$ satisfies Carath\'{e}odory condition (i.e. measurable in $s$ for all $t \in~[0,1]$ and continuous in $t$ for all $s \in [0,1] $) such that $k(t,s)m_2(s)\in L_1 \forall t\in[0,1].$
 1 1 857 . . 2008-08-24 2009-08-17 312 yes 398 no 438 1 2009 52 0 Approximation of solutions of nonlinear heat transfer problems
We develop a generalized approximation method (GAM) to obtain solution of a steady state one-dimensional nonlinear convective-radiative-conduction equation. The GAM generates a bounded monotone sequence of solutions of linear problems. The sequence of approximants converges monotonically and rapidly to a solution of the original problem. We present some numerical simulation to illustrate and confirm our results.
 1 13 107 . .
2009-08-25 2009-04-21 221 yes 439 1 2009 53 0 Resonant problem for a class of BVPs on the half-line
We provide an existence result for a Neumann nonlinear boundary value problem posed on the half-line. Our main tool is the multi-valued version of the Miranda Theorem.
 1 10 71 . .
2009-08-26 2009-03-05 1207 yes 511 no 441 1 2009 54 0 On $\Psi$-stability of nonlinear Lyapunov matrix differential equations
We prove necessary and sufficient conditions for $\Psi -$ (uniform) stability of the trivial solution of a nonlinear Lyapunov matrix differential equation.
 1 18 79 . .
2009-09-12 2009-06-14 1389 yes 442 1 2009 55 0 Positive solutions of a second-order three-point boundary value problem via functional compression-expansion
This paper examines a three point, nonlocal boundary value problem for a second order ordinary differential equation. We make use of a generalization of the fixed point theorem of compression and expansion of functional type to obtain the existence of positive solutions.
 1 8 7 . .
2009-09-14 2009-07-14 512 yes 443 1 2009 56 0 Positive solutions for singular $\phi-$Laplacian BVPs on the positive half-line
In this work, we are concerned with the existence of positive solutions for a $\phi$ Laplacian boundary value problem on the half-line. The results are proved using the fixed point index theory on cones of Banach spaces and the upper and lower solution technique. The nonlinearity may exhibit a singularity at the origin with respect to the solution. This singularity is treated by regularization and approximation together with compactness and sequential arguments.
 1 24 70 . .
2009-10-08 2009-06-27 1008 yes 513 no 444 1 2009 57 0 Solvability of a one-dimensional quasilinear problem under nonresonance conditions on the potential
Problem of the type $-\Delta_{p}u=f(u)+h(x) \textrm{ in } (a, b) $ with $u=0$ on $ \{a,b\} $ is solved under nonresonance conditions stated with respect to the first eigenvalue and the first curve in the Fu\v{c}ik spectrum of $(-\Delta_{p},W_{0}^{1,p}(a,b))$, only on a primitive of $f$.
 1 29 24 . .
2009-11-02 2008-08-07 514 yes 445 1 2009 58 0 Spectral asymptotics for inverse nonlinear Sturm-Liouville problems
We consider the nonlinear Sturm-Liouville problem
$$
-u''(t) + f(u(t), u'(t)) = \lambda u(t),
\enskip u(t) > 0,
\quad t \in I := (-1/2, 1/2), \enskip u(\pm 1/2) = 0,
$$
where $f(x, y) = \vert x\vert^{p-1}x - \vert y\vert^m$, $p > 1, 1 \le m < 2$ are constants and $\lambda > 0$ is an eigenvalue parameter. To understand well the global structure of the bifurcation branch of positive solutions in $\mbox{\bf R}_+ \times L^q(I)$ ($1 \le q < \infty$) from a viewpoint of inverse problems, we establish the precise asymptotic formulas for the eigenvalue $\lambda = \lambda_q(\alpha)$ as $\alpha :=\Vert u_\lambda\Vert_q \to \infty$, where $u_\lambda$ is a solution associated with given $\lambda > \pi^2$.
1 18 414 . .
2009-11-02 2009-08-04 515 yes 446 1 2009 59 0 An optimal condition for the uniqueness of a periodic solution for linear functional differential systems
Unimprovable effective efficient conditions are established for the unique solvability of the periodic problem
$$
\begin{aligned}
u'_i (t)&=\sum\limits_{j=2}^{i+1} \ell_{i,j}(u_{j})(t) + q_i(t) \qquad \text{for} \quad 1 \leq i\leq n-1,\\
u'_n (t)&=\sum\limits_{j=1}^{n} \ell_{n,j}(u_{j} )(t) + q_n(t),\\
u_j (0)& = u_j (\omega) \qquad \text{for} \quad 1 \leq j\leq n,
\end{aligned}
$$
where $\omega >0$, $\ell_{ij}:C([0,\omega])\to L([0,\omega])$ are linear bounded operators, and
$q_i \in L([0,\omega])$.
 1 12 11 . .
2009-11-03 2009-07-30 516 yes 517 no 447 1 2009 60 0 Forced oscillation of second-order nonlinear dynamic equations on time scales
In this paper, by defining a class of functions, we establish some oscillation criteria for the second order nonlinear dynamic equations with forced term $$ x^{\Delta\Delta}(t)+a(t)f(x(q(t)))=e(t) $$ on a time scale $\mathbb{T}.$ Our results unify the oscillation of the second order forced differential equation and the second order forced difference equation. An example is considered to illustrate the main results.
 1 8 107 . .
2009-11-03 2009-08-26 518 yes 519 no 520 no 521 no 448 1 2009 61 0 Oscillation criteria for a certain second-order nonlinear differential equations with deviating arguments
In this paper, by using the generalized Riccati technique and the integral averaging technique, some new oscillation criteria for certain second order retarded differential equation of the form
\begin{equation*}
\left( r\left( t\right) \left\vert u^{\prime }\left( t\right) \right\vert
^{\alpha -1}u^{\prime }\left( t\right) \right) ^{\prime }+p\left( t\right)
f\left( u\left( \tau \left( t\right) \right) \right) =0
\end{equation*}
are established. The results obtained essentially improve known results in the literature and can be applied to the well known half-linear and Emden-Fowler type equations.
 1 11 857 . .
2009-11-03 2009-10-17 522 yes 449 1 2009 62 0 On $Psi$-bounded solutions for non-homogeneous matrix Lyapunov systems on $R$
In this paper we provide necesssary and sufficient conditions for the existence of at least one $\Psi$-bounded solution on $\mathbb{R}$ for the system $X'=A(t)X +XB(t)+F(t)$, where $F(t)$ is a Lebesgue $\Psi$-integrable matrix valued function on $\mathbb{R}$. Further, we prove a result relating to the asymptotic behavior of the $\Psi$-bounded solutions of this system.
 1 12 79 . .
2009-11-06 2009-06-18 523 yes 524 no 450 1 2009 63 0 Oscillation of solutions of some higher order linear differential equations
In this paper, we deal with the order of growth and the hyper order of solutions of higher order linear differential equations $$f^{(k)}+B_{k-1}f^{(k-1)}+\cdots+B_1f'+B_0f=F$$ where $B_j(z) (j=0,1,\ldots,k-1)$ and $F$ are entire functions or polynomials. Some results are obtained which improve and extend previous results given by Z.-X. Chen, J. Wang, T.-B. Cao and C.-H. Li.
 1 18 107 . .
2009-11-07 2009-06-08 525 yes 526 no 451 1 2009 64 0 Oscillatory and asymptotic behavior of fourth order quasilinear difference equations
The authors consider the fourth order quasilinear difference equation $$\Delta^{2}\left(p_{n}|\Delta^{2}x_n|^{\alpha-1}\Delta^{2}x_n\right)+q_{n}|x_{n+3}|^{\beta -1}x_{n+3}=0,$$ where $\alpha$ and $\beta$ are positive constants, and ${\{p_{n}\}}$ and ${\{q_{n}\}}$ are positive real sequences. They obtain sufficient conditions for oscillation of all solutions when $\sum\limits_{n=n_{0}}^{\infty}\left(\frac{n}{p_{n}}\right)^\frac{1}{\alpha}<\infty $ and $\sum\limits_{n=n_{0}}^{\infty}\left(\frac{n}{{p_{n}}^{\frac{1}{\alpha}}}\right)<\infty.$ The results are illustrated with examples.
 1 15 107 . .
2009-11-25 2009-08-08 244 yes 527 no 452 1 2009 65 0 Lower bounds and positivity conditions for Green's functions to second order differential-delay equations
We consider the Cauchy problem on the positive half-line for the differential-delay equation
$$
\ddot u(t)+2c_0(t)\dot u(t)+c_1(t)\dot u(t-h)+d_0(t)u(t)+d_1(t)u(t-h)+d_2(t)u(t-2h)=0
$$
where $c_k(t), d_j(t) (t\geq 0; k=0,1; j=0,1,2)$ are continuous functions. Conditions providing the positivity of the Green function and a lower bound for that function are derived. Our results are new even in the case of ordinary differential equations. Applications of the obtained results to equations with nonlinear causal mappings are also discussed. Equations with causal mappings include ordinary differential and integro-differential equations. In addition, we establish positivity conditions for solutions of functional differential equations with variable and distributed delays.
 1 11 107 . .
2009-12-05 2009-09-25 366 yes 453 1 2009 66 0 Oscillation of complex high order linear differential equations with coefficients of finite iterated order
In this paper, we investigate the growth of solutions of complex high order linear differential equations with entire or meromorphic coefficients of finite iterated order and we obtain some results which improve and extend some previous results of Z. X. Chen and L. Kinnunen.
 1 13 107 . .
2009-12-05 2009-07-18 528 yes 529 no 454 1 2009 67 0 Existence, uniqueness and stability results of impulsive stochastic semilinear neutral functional differential equations with infinite delays
This article presents the results on existence, uniqueness and stability of mild solutions of impulsive stochastic semilinear neutral functional differential equations without a Lipschitz condition and with a Lipschitz condition. The results are obtained by using the method of successive approximations.
 1 13 7 . .
2009-12-05 2009-06-22 530 yes 531 no 455 1 2009 68 0 Periodic solutions of p-Laplacian systems with a nonlinear convection term
In this work, we study the existence of periodic solutions for the evolution of p-Laplacian system and we show that these periodic solutions belong to $L^{\infty}(\omega, W^{1,\infty}(\Omega))$ and give a bound of $\left \Vert \nabla u_{i}(t)\right \Vert_{\infty}$ under certain geometric conditions on $\partial \Omega$.
 1 10 16 . .
2009-12-25 2009-03-15 149 yes 456 1 2009 69 0 Existence and uniqueness of solution for fractional differential equations with integral boundary conditions
This paper is devoted to the existence and uniqueness results of solutions for fractional differential equations with integral boundary conditions.
$$
\left\{
\begin{array}{l}
^C\hspace{-0.2em}D^\alpha x(t)+f(t,x(t),x'(t))=0,\quad t\in(0,1),\\
x(0)=\int^1_0 g_0(s,x(s))\mathrm{d}s ,\\
x(1)=\int^1_0 g_1(s,x(s))\mathrm{d}s ,\\
x^{(k)}(0)=0,\,\ k=2,3,\cdots, [\alpha]-1.
\end{array} \right.
$$
By means of the Banach contraction mapping principle, some new results on the existence and uniqueness are obtained. It is interesting to note that the sufficient conditions for the existence and uniqueness of solutions are dependent on the order $\alpha$.
 1 10 107 . .
2009-12-25 2009-08-12 333 yes 450 no 532 no 457 1 2009 70 0 Three point boundary value problem for singularly perturbed semilinear differential equations
In this paper, we investigate the problem of existence and asymptotic behavior of solutions for the nonlinear boundary value problem
\begin{eqnarray*}
\epsilon y''+ky=f(t,y),\quad t\in\langle a,b \rangle, \quad k<0,\quad 0<\epsilon<<1
\end{eqnarray*}
satisfying three point boundary conditions. Our analysis relies on the method of lower and upper solutions.
 1 4 16 . .
2009-12-25 2008-12-17 533 yes 458 1 2009 71 0 Existence of solutions for a nonlinear fractional order differential equation
Let $D^\alpha$ denote the Riemann-Liouville fractional differential operator of order $\alpha$. Let $1 < \alpha < 2$ and $0 < \beta < \alpha$. Define the operator $L$ by $L = D^\alpha - a D^\beta$ where $a \in \mathbb{R}$. We give sufficient conditions for the existence of solutions of the nonlinear fractional boundary value problem
\begin{eqnarray*}
&&Lu(t) + f(t, u(t)) = 0, \quad 0 < t < 1,\\
&&u(0) = 0, \, u(1)= 0.
\end{eqnarray*}
 1 9 107 . .
2009-12-25 2009-07-28 230 yes 534 no 459 1 2009 72 0 On a nonstandard Volterra type dynamic integral equation on time scales
The main objective of the present paper is to study some basic qualitative properties of solutions of a nonstandard Volterra type dynamic integral equation on time scales. The tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain integral inequality with explicit estimate on time scales.
 1 14 71 . .
2009-12-25 2009-08-15 535 yes 460 1 2009 73 0 Existence of global solutions for a system of reaction-diffusion equations with exponential nonlinearity
We consider the question of global existence and uniform boundedness of nonnegative solutions of a system of reaction-diffusion equations with exponential nonlinearity using Lyapunov function techniques.
 1 7 414 . .
2009-12-28 2009-08-31 536 yes 461 1 2010 1 0 Some stability and boundedness conditions for non-autonomous differential equations with deviating arguments
In this article, the author studies the stability and boundedness of solutions for the non-autonomous third order differential equation with a deviating argument, $r$:
\begin{equation*}
\begin{array}{c}
x^{\prime \prime \prime }(t)+a(t)x^{\prime \prime }(t)+b(t)g_{1}(x^{\prime}(t-r))+g_{2}(x^{\prime}(t))+h(x(t-r)) \\
=p(t,x(t),x(t-r),x^{\prime }(t),x^{\prime }(t-r),x^{\prime \prime }(t)),
\end{array}
\end{equation*}
where $r>0$ is a constant. Sufficient conditions are obtained; a stability result in the literature is improved and extended to the preceding equation for the case $p(t,x(t),x(t-r),x^{\prime }(t),x^{\prime}(t-r),x^{\prime \prime }(t))=0,$ and a new boundedness result is also established for the case $p(t,x(t),x(t-r),x^{\prime }(t),x^{\prime}(t-r),x^{\prime \prime }(t))\neq 0.$
 1 12 71 . .
2010-01-05 2009-05-11 537 yes 462 1 2010 2 0 Existence results for a class of nonlinear parabolic equations in Orlicz spaces
An existence result of a renormalized solution for a class of nonlinear parabolic equations in Orlicz spaces is proved. No growth assumption is made on the nonlinearities.
 1 19 16 . .
2010-01-05 2009-06-11 334 yes 463 1 2010 3 0 Existence of extremal solutions of a three-point boundary value problem for a general second order p-Laplacian integro-differential equation
In this paper, we prove the existence of extremal positive, concave and pseudo-symmetric solutions for a general three-point second order p-Laplacian integro-differential boundary value problem by using an abstract monotone iterative technique.
 1 9 107 . .
2010-01-06 2009-07-20 307 yes 308 no 464 1 2010 4 0 Existence of solutions of abstract fractional impulsive semilinear evolution equations
In this paper we prove the existence of solutions of fractional impulsive semilinear evolution equations in Banach spaces. A nonlocal Cauchy problem is discussed for the evolution equations. The results are obtained using fractional calculus and fixed point theorems. An example is provided to illustrate the theory.
 1 12 71 . .
2010-01-08 2009-07-11 538 yes 540 no 465 1 2010 5 0 Existence of a positive solution to a right focal boundary value problem
In this paper we apply the recent extension of the Leggett-Williams Fixed Point Theorem which requires neither of the functional boundaries to be invariant to the second order right focal boundary value problem. We demonstrate a technique that can be used to deal with a singularity and provide a non-trivial example.
 1 6 107 . .
2010-01-05 2009-11-23 481 yes 57 no 322 no 466 1 2010 6 0 Positive almost periodic solutions for a class of nonlinear Duffing equations with a deviating argument
In this paper, we study a class of nonlinear Duffing equations with a deviating argument and establish some sufficient conditions for the existence of positive almost periodic solutions of the equation. These conditions are new and complement to previously known results.
 1 12 25 . .
2010-01-08 2009-03-18 541 yes 542 no 467 1 2010 7 0 Function bounds for solutions of Volterra integro dynamic equations on time scales
Introducing shift operators on time scales we construct the integro-dynamic equation corresponding to the convolution type Volterra differential and difference equations in particular cases $\mathbb{T}=\mathbb{R}$ and
$\mathbb{T}=\mathbb{Z}$. Extending the scope of time scale variant of Gronwall's inequality we determine function bounds for the solutions of the integro dynamic equation.
 1 22 107 . .
2010-01-08 2009-09-23 472 yes 468 1 2010 8 0 Anti-periodic solutions for a class of third-order nonlinear differential equations with a deviating argument
In this paper, we study a class of third-order nonlinear differential equations with a deviating argument and establish some sufficient conditions for the existence and exponential stability of anti-periodic solutions of the equation. These conditions are new and complement to previously known results.
 1 12 25 . .
2010-01-08 2009-03-17 543 yes 542 no 544 no 545 no 469 1 2010 9 0 Singularly perturbed semilinear Neumann problem with non-normally hyperbolic critical manifold
In this paper, we investigate the problem of existence and asymptotic behavior of the solutions for the nonlinear boundary value problem
\begin{eqnarray*}
\epsilon y''+ky=f(t,y),\quad t\in\langle a,b \rangle, \quad k>0,\quad 0<\epsilon<<1
\end{eqnarray*}
satisfying Neumann boundary conditions and where critical manifold is not normally hyperbolic. Our analysis relies on the method upper and lower solutions.
 1 11 107 . .
2010-01-12 2009-08-26 533 yes 470 1 2010 10 0 A Liapunov functional for a linear integral equation
In this note we consider a scalar integral equation $x(t)= a(t)-\int^t_0 C(t,s)x(s)ds$, together with its resolvent equation, $R(t,s)= C(t,s)-\int^t_s C(t,u) R(u,s)du$, where $C$ is convex. Using a Liapunov functional we show that for fixed $s$ then $|R(t,s) - C(t,s)| \to 0$ as $t \to \infty$ and $\int^{\infty}_s (R(t,s)-C(t,s))^2 dt < \infty$. We then show that the variation of parameters formula $x(t)=a(t)-\int^t_0 R(t,s) a(s)ds$ can be replaced by $X(t)=a(t)-\int^t_0 C(t,s)a(s)ds$ when $a \in L^1[0,\infty)$ and that $|X(t) - x(t)|\to 0$ as $t \to \infty$ and $\int^{\infty}_0 (x(t)-X(t))^2 dt < \infty$. A mild nonlinear extension is given.
 1 10 3 . .
2010-02-28 2009-11-17 857 yes 471 1 2010 11 0 Linear impulsive dynamic systems on time scales
The purpose of this paper is to present the fundamental concepts of the basic theory for linear impulsive systems on time scales. First, we introduce the transition matrix for linear impulsive dynamic systems on time scales and we establish some properties of them. Second, we prove the existence and uniqueness of solutions for linear impulsive dynamic systems on time scales. Also we give some sufficient conditions for the stability of linear impulsive dynamic systems on time scales.
 1 30 70 . .
2010-03-01 2009-08-30 546 yes 457 no 472 1 2010 12 0 On some qualitative behaviors of solutions to a kind of third order nonlinear delay differential equations
Sufficiency criteria are established to ensure the asymptotic stability and boundedness of solutions to third-order nonlinear delay differential equations of the form
\begin{equation*}
\begin{array}{c}
\dddot{x}(t)+e(x(t),\dot{x}(t),\ddot{x}(t))\ddot{x}(t)+g(x(t-r),\dot{x}
(t-r))+\psi (x(t-r)) \\
=p(t,x(t),x(t-r),x^{\prime }(t),x^{\prime }(t-r),x^{\prime \prime }(t)).
\end{array}
\end{equation*}
By using Lyapunov's functional approach, we obtain two new results on the subject, which include and improve some related results in the relevant literature. Two examples are also given to illustrate the importance of results obtained.
 1 19 7 . .
2010-03-08 2009-08-13 537 yes 473 1 2010 13 0 On the singular behavior of solutions of a transmission problem in a dihedral
In this paper, we study the singular behavior of solutions of a boundary value problem with mixed conditions in a neighborhood of an edge. The considered problem is defined in a nonhomogeneous body of $\mathbb{R}^{3}$, this is done in the general framework of weighted Sobolev spaces. Using the results of Benseridi-Dilmi, Grisvard and Aksentian, we show that the study of solutions' singularities in the spatial case becomes a study of two problems: a problem of plane deformation and the other is of normal plane deformation.
 1 12 79 . .
2010-03-15 2009-06-24 547 yes 548 no 474 1 2010 14 0 Existence of solutions for a class of fourth-order m-point boundary value problems
Some existence criteria are established for a class of fourth-order $m$-point boundary value problem by using the upper and lower solution method and the Leray-Schauder continuation principle.
 1 8 107 . .
2010-03-15 2009-10-08 549 yes 550 no 475 1 2010 15 0 Extinction and non-extinction of solutions for a nonlocal reaction-diffusion problem
We investigate extinction properties of solutions for the homogeneous Dirichlet boundary value problem of the nonlocal reaction-diffusion equation $u_t-d\Delta u+k u^p=\int_\Omega u^q(x,t)\,dx$ with $p, q\in (0, 1)$ and $k, d >0$. We show that $q=p$ is the critical extinction exponent. Moreover, the precise decay estimates of solutions before the occurrence of the extinction are derived.
 1 12 107 . .
2010-03-16 2009-06-18 551 yes 476 1 2010 16 0 On existence and uniqueness of positive solutions for integral boundary boundary value problems
By applying the monotone iterative technique, we obtain the existence and uniqueness of $C^1[0,1]$ positive solutions in some set for singular boundary value problems of second order ordinary differential equations with integral boundary conditions.
 1 8 414 . .
2010-03-16 2010-01-01 552 yes 553 no 554 no 477 1 2010 17 0 Multiple positive solutions for boundary value problems of second-order differential equations system on the half-line
In this paper, we study the existence of positive solutions for boundary value problems of second-order differential equations system with integral boundary condition on the half-line. By using a three functionals fixed point theorem in a cone and a fixed point theorem in a cone due to Avery-Peterson, we show the existence of at least two and three monotone increasing positive solutions with suitable growth conditions imposed on the nonlinear terms.
 1 15 414 . .
2010-03-16 2009-12-28 449 yes 450 no 451 no 478 1 2010 18 0 On the viscous Burgers equation in unbounded domain
In this paper we investigate the existence and uniqueness of global solutions, and a rate stability for the energy related with a Cauchy problem to the viscous Burgers equation in unbounded domain $\re\times(0,\infty)$. Some aspects associated with a Cauchy problem are presented in order to employ the approximations of Faedo-Galerkin in whole real line $\re$. This becomes possible due to the introduction of weight Sobolev spaces which allow us to use arguments of compactness in the Sobolev spaces.
 1 23 857 . .
2010-04-08 2009-12-29 219 yes 163 no 220 no 479 1 2010 19 0 Dynamic analysis of an impulsively controlled predator-prey system
In this paper, we study an impulsively controlled predator-prey model with Monod-Haldane functional response. By using the Floquet theory, we prove that there exists a stable prey-free solution when the impulsive period is less than some critical value, and give the condition for the permanence of the system. In addition, we show the existence and stability of a positive periodic solution by using bifurcation theory.
 1 14 281 . .
2010-04-17 2009-07-15 878 yes 480 1 2010 20 0 Multiple positive solutions of nonlinear singular m-point boundary value problem for second-order dynamic equations with sign changing coefficients on time scales
Let $\mathbb{T}$ be a time scale. In this paper, we study the existence of multiple positive solutions for the following nonlinear singular $m$-point boundary value problem dynamic equations with sign changing coefficients on time scales

$$\left\{\begin{array}{lll}
u^{\triangle\nabla}(t)+ a(t)f(u(t))=0, (0,T)_{\mathbb{T}},
\cr\
u^{\triangle}(0)=\sum_{i=1}^{m-2}a_{i}u^{\triangle}(\xi_i),
\cr
u(T)=\sum_{i=1}^{k}b_{i}u(\xi_i)-\sum_{i=k+1}^{s}b_{i}u(\xi_i)-\sum_{i=s+1}^{m-2}b_{i}u^{\triangle}(\xi_i),
\end{array}\right.$$

where $1\leq k\leq s\leq m-2, a_i, b_i\in(0,+\infty)$ with $0<\sum_{i=1}^{k}b_{i}-\sum_{i=k+1}^{s}b_{i}<1,
0<\sum_{i=1}^{m-2}a_{i}<1, 0<\xi_1<\xi_2<\cdots<\xi_{m-2}<\rho(T)$, $f\in C( [0,+\infty),[0,+\infty))$, $a(t)$ may be singular at $t=0$. We show that there exist two positive solutions by using two different fixed point theorems respectively. As an application, some examples are included to illustrate the main results. In particular, our criteria extend and improve some known results.
 1 13 70 . .
2010-04-17 2010-01-13 556 yes 481 1 2010 21 0 General existence results for nonconvex third order differential inclusions
In this paper we prove the existence of solutions to the following third order differential inclusion:
$$\left\{
\begin{array}{ll} x^{(3)}(t)\in
F(t,x(t),\dot{x}(t),\ddot{x}(t))+G(x(t),\dot{x}(t),\ddot{x}(t)),
\mbox{ a.e. on } [0,T]\cr x(0)=x_0, \dot x(0)=u_0, \ddot
x(0)=v_0, \mbox{ and }\ddot{x}(t)\in S, \forall t\in [0,T],
\end{array}\right.
$$
where $F:[0,T]\times \mathbb{H}\times \mathbb{H} \times \mathbb{H}\rightarrow \mathbb{H}$ is a continuous set-valued mapping, $G:\mathbb{H}\times \mathbb{H} \times \mathbb{H}\rightarrow \mathbb{H}$ is an upper semi-continuous set-valued mapping with $G(x,y,z)\subset \partial^C g(z)$ where $g: \mathbb{H}\rightarrow \mathbb{R}$ is a uniformly regular function over $S$ and locally Lipschitz and $S$ is a ball compact subset of a separable Hilbert space $\mathbb{H}$.
 1 10 107 . .
2010-04-19 2009-07-10 557 yes 558 no 482 1 2010 22 0 Existence of almost automorphic solutions to some classes of nonautonomous higher-order differential equations
In this paper, we obtain the existence of almost automorphic solutions to some classes of nonautonomous higher order abstract differential equations with Stepanov almost automorphic forcing terms. A few illustrative examples are discussed at the very end of the paper.
 1 26 70 . .
2010-05-03 2010-02-08 947 yes 483 1 2010 23 0 A priori estimate for discontinuous solutions of a second order linear hyperbolic problem
In the paper we investigate a non-local contact-boundary value problem for a system of second order hyperbolic equations with discontinuous solutions. Under some conditions on input data, a priori estimate is obtained for the solution of this problem.
 1 12 11 . .
2010-05-04 2008-11-19 559 yes 484 1 2010 24 0 Boundedness of solutions to a retarded Liénard equation
This paper is concerned with the following retarded Li\'{e}nard equation

$$x''(t)+f_1(x(t))(x'(t))^2+f_2(x(t))x'(t)+g_1(x(t))+g_2(x(t-\tau(t)))=e(t).$$

We prove a new theorem which ensures that all solutions of the above Li\'{e}nard equation satisfying given initial conditions are bounded. As one will see, our results improve some earlier results even in the case of $f_1(x)\equiv 0$.
 1 9 25 . .
2010-05-05 2009-09-14 560 yes 561 no 485 1 2010 25 0 Oscillation criteria for second order nonlinear perturbed differential equations
Sufficient conditions for the oscillation of the nonlinear second order differential equation $(a(t)x^{\prime })^{\prime }+Q(t,x^{\prime})=P(t,x,x^{\prime })$ are established where the coefficients are continuous and $a(t)$ is nonnegative.
 1 11 7 . .
2010-05-05 2009-06-23 562 yes 486 1 2010 26 0 The upper and lower solution method for nonlinear third-order three-point boundary value problem
This paper is concerned with the following nonlinear third-order three-point boundary value problem

\[\left\{
\begin{array}{l}
u^{\prime \prime \prime }(t)+f\left( t,u\left( t\right) ,u^{\prime}\left(t\right) \right) =0,\, t\in \left[ 0,1\right], \\
u\left( 0\right) =u^{\prime }\left( 0\right) =0,\, u^{\prime}\left( 1\right) =\alpha u^{\prime }\left( \eta \right),\label{1.1}
\end{array}
\right.\]

where $0<\eta <1$ and $0\leq \alpha <1.$ A new maximum principle is established and some existence criteria are obtained for the above problem by using the upper and lower solution method.
 1 8 7 . .
2010-05-06 2009-12-17 549 yes 550 no 563 no 487 1 2010 27 0 Multiplicity of positive solutions for a fourth-order quasilinear singular differential equation
This paper is concerned with the multiplicity of positive solutions of boundary value problem for the fourth-order quasilinear singular differential equation
$$
(|u''|^{p-2}u'')''=\lambda g(t)f(u),\quad 0<t<1,
$$
where $p>1$, $\lambda>0$. We apply the fixed point index theory and the upper and lower solutions method to investigate the multiplicity of positive solutions. We have found a threshold $\lambda^*<+\infty$, such that if $0<\lambda\leq\lambda^*$, then the problem admits at least one positive solution; while if $\lambda \lambda^*$, then the problem has no positive solution. In particular, there exist at least two positive solutions for $0<\lambda<\lambda^*$.
 1 15 7 . .
2010-05-26 2009-12-28 1306 yes 134 no 564 no 488 1 2010 28 0 Higher order multi-point boundary value problems with sign-changing nonlinearities and nonhomogeneous boundary conditions
We study classes of $n$th order boundary value problems consisting of an equation having a sign-changing nonlinearity $f(t,x)$ together with several different sets of nonhomogeneous multi-point boundary conditions. Criteria are established for the existence of nontrivial solutions, positive solutions, and negative solutions of the problems under consideration. Conditions are determined by the behavior of $f(t,x)/x$ near $0$ and $\pm\infty$ when compared to the smallest positive characteristic values of some associated linear integral operators. This work improves and extends a number of recent results in the literature on this topic. The results are illustrated with examples.
 1 40 414 . .
2010-05-31 2010-04-01 7 yes 489 no 497 no 330 no 489 1 2010 29 0 Existence results for a  partial neutral integro-differential equation with state-dependent delay
In this paper we study the existence of mild solutions for a class of abstract partial neutral integro-differential equations with state-dependent delay.
 1 12 70 . .
2010-06-02 2010-02-06 446 yes 490 1 2010 30 0 Existence of positive solutions for boundary value problems of fractional functional differential equations
This paper deals with the existence of positive solutions for a boundary value problem involving a nonlinear functional differential equation of fractional order $\alpha$ given by $ D^{\alpha} u(t) + f(t, u_t) = 0$, $t \in (0, 1)$, $2 < \alpha \le 3$, $ u^{\prime}(0) = 0$, $u^{\prime}(1) = b u^{\prime}(\eta)$, $u_0 = \phi$. Our results are based on the nonlinear alternative of Leray-Schauder type and Krasnosel'skii fixed point theorem.
 1 14 70 . .
2010-06-03 2010-01-21 351 yes 492 1 2010 31 0 Homoclinic solutions for a class of non-periodic second order Hamiltonian systems
We study the existence of homoclinic solutions for the second order Hamiltonian system $\ddot{u}+V_{u}(t,u)=f(t)$. Let $V(t,u)=-K(t,u)+W(t,u)\in C^{1}(\mathbb{R}\times\mathbb{R}^{n}, \mathbb{R})$ be $T$-periodic in $t$, where $K$ is a quadratic growth function and $W$ may be asymptotically quadratic or super-quadratic at infinity. One homoclinic solution is obtained as a limit of solutions of a sequence of periodic second order differential equations.
 1 11 16 . .
2010-06-03 2009-11-08 566 yes 567 no 568 no 493 1 2010 32 0 Iterated order of solutions of linear differential equations with entire coefficients
In this paper, we investigate the iterated order of solutions of higher order homogeneous linear differential equations with entire coefficients. We improve and extend some results of Belaidi and Hamouda by using the concept of the iterated order. We also consider nonhomogeneous linear differential equations.
 1 17 107 . .
2010-06-03 2009-12-15 569 yes 1377 no 491 1 2010 33 0 Existence of multiple positive solutions of higher order multi-point nonhomogeneous boundary value problem
In this paper, by using the Avery and Peterson fixed point theorem, we establish the existence of multiple positive solutions for the following higher order multi-point nonhomogeneous boundary value problem
$ u^{(n)}(t) + f(t,u(t),u'(t),\ldots,u^{(n-2)}(t)) = 0, t\in (0,1)$,
$ u(0)= u'(0)=\cdots=u^{(n-3)}(0)=u^{(n-2)}(0)=0, u^{(n-2)}(1)-\sum_{i=1}^{m} a_i u^{(n-2)}(\xi_i)=\lambda$,
where $n\ge3$ and $m\ge1$ are integers, $0<\xi_1<\xi_2<\cdots<\xi_m<1$ are constants, $\lambda\in [0,\infty)$ is a parameter, $a_i>0$ for $1\le i\le m$ and $\sum_{i=1}^{m} a_i\xi_i<1$, $f(t,u,u',\cdots,u^{(n-2)})\in C([0,1]\times[0,\infty)^{n-1}, [0,\infty))$. We give an example to illustrate our result.
 1 13 414 . .
2010-06-07 2010-04-08 352 yes 353 no 351 no 494 1 2010 34 0 Effect of nonlinear perturbations on second order linear nonoscillatory differential equations
The aim of this paper is to show that any second order nonoscillatory linear differential equation can be converted into an oscillating system by applying a sufficiently large nonlinear perturbation. This can be achieved through a detailed analysis of possible nonoscillatory solutions of the perturbed differential equation which may exist when the perturbation is sufficiently small. As a consequence the class of oscillation-generating perturbations is determined precisely with respect to the original nonoscillatory linear equation.
 1 16 11 . .
2010-06-10 2010-01-10 570 yes 571 no 495 1 2010 35 0 Picone type formula for non-selfadjoint impulsive differential equations with discontinuous solutions
A Picone type formula for second order linear non-selfadjoint impulsive differential equations with discontinuous solutions having fixed moments of impulse actions is derived. Applying the formula, Leighton and Sturm-Picone type comparison theorems as well as several oscillation criteria for impulsive differential equations are obtained.
 1 12 7 . .
2010-06-10 2009-12-26 572 yes 573 no 496 1 2010 36 0 Multiple positive solutions for (n-1, 1)-type semipositone conjugate boundary value problems of nonlinear fractional differential equations
In this paper, we consider (n-1, 1)-type conjugate boundary value problem for the nonlinear fractional differential equation
\begin{gather*}\begin{array}{ll}
\mathbf{D}_{0+}^\alpha u(t)+\lambda f(t,u(t))=0,\quad 0<t<1, \lambda >0,\\
u^{(j)}(0)=0, 0\leq j\leq n-2,\\
u(1)=0,
\end{array}\end{gather*}
where $\lambda$ is a parameter, $\alpha\in(n-1, n]$ is a real number and $n\geq 3$, and $\mathbf{D}_{0+}^\alpha$ is the Riemann-Liouville's fractional derivative, and $f$ is continuous and semipositone. We give properties of Green's function of the boundary value problems, and derive an interval of $\lambda$ such that any $\lambda$ lying in this interval, the semipositone boundary value problem has multiple positive solutions.
 1 12 107 . .
2010-06-10 2009-07-28 574 yes 497 1 2010 37 0 On solutions of some fractional $m$-point boundary value problems at resonance
In this paper, the following fractional order ordinary differential equation boundary value problem:
\begin{gather*}
D_{0+}^\alpha u(t) =f(t,u(t),D_{0+}^{\alpha-1}u(t))+e(t), 0<t<1,\\
I_{0+}^{2-\alpha}u(t)\mid_{t=0}=0, D_{0+}^{\alpha-1}u(1)=\sum_{i=1}^{m-2}\beta_i D_{0+}^{\alpha-1}u(\eta_i),
\end{gather*}
is considered, where $1< \alpha \leq 2,$ is a real number, $D_{0+}^\alpha$ and $I_{0+}^{\alpha}$ are the standard Riemann-Liouville differentiation and integration, and $f:[0,1]\times R^2 \to R$ is continuous and $e \in L^1[0,1]$, and $\eta_i \in (0, 1), \beta_i \in R, i=1,2, \cdots, m-2$, are given constants such that $\sum_{i=1}^{m-2}\beta_i=1$. By using the coincidence degree theory, some existence results of solutions are established.
 1 15 107 . .
2010-06-16 2009-12-20 575 yes 498 1 2010 38 0 Multiple positive solutions for second order impulsive boundary value problems in Banach spaces
By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.
 1 15 25 . .
2010-06-19 2009-12-29 576 yes 577 no 1115 no 499 1 2010 39 0 Multiple positive solutions for a nonlinear 2n-th order m-point boundary value problems
In this paper, we consider the existence of multiple positive solutions for the 2n-th order $m$-point boundary value problems:
$$\left\{\begin{array}{ll} x^{(2n)}(t)=f(t,x(t),x^{''}(t),\cdots ,x^{(2(n-1))}(t)), 0\leq t\leq 1,\\
x^{(2i+1)}(0)=\sum\limits_{j=1}^{m-2}\alpha_{ij}x^{(2i+1)}(\xi_j),\quad
x^{(2i)}(1)=\sum\limits_{j=1}^{m-2}\beta_{ij}x^{(2i)}(\xi_j), 0\leq i\leq n-1,\\
\end{array}\right.$$
where $\alpha_{ij}, \beta_{ij} \ (0\leq i\leq n-1,1\leq j\leq m-2) \in [0,\infty)$, $\sum\limits_{j=1}^{m-2}\alpha_{ij},\sum\limits_{j=1}^{m-2}\beta_{ij}\in (0,1)$, $0<\xi_1<\xi_2<\ldots<\xi_{m-2}<1$. Using Leggett-Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem.
 1 13 7 . .
2010-06-23 2010-03-26 460 yes 579 no 580 no 500 1 2010 40 0 Some properties of solutions for a class of metaparabolic equations
In this paper, we study the initial boundary value problem for a class of metaparabolic equations. We establish the existence of solutions by the energy techniques. Some results on the regularity, blow-up and existence of global attractor are obtained.
 1 14 281 . .
2010-07-15 2010-01-10 135 yes 581 no 2089 no 501 1 2010 41 0 Existence theorems for second order multi-point boundary value problems
We are interested in the existence of nontrivial solutions for the second order nonlinear differential equation (E): $y'' (t) = f\big(t, y (t)\big) = 0, 0 < t < 1$ subject to multi-point boundary conditions at $t=1$ and either Dirichlet or Neumann conditions at $t=0$. Assume that $f(t, y)$ satisfies $|f(t, y)| \le k(t) |y| + h(t)$ for non-negative functions $k, h \in L^1 (0, 1)$ for all $(t, y) \in (0, 1) \times \Bbb R$ and $f(t, 0) \not\equiv 0$ for $t\in (0, 1)$. We show without any additional assumption on $h(t)$ that if $\|k\|_1$ is sufficiently small where $\|\cdot \|_1$ denotes the norm of $L^1(0, 1)$ then there exists at least one non-trivial solution for such boundary value problems. Our results reduce to that of Sun and Liu and Sun for the three point problem with Neumann boundary condition at $t=0$.
 1 12 858 . .
2010-07-29 2009-12-14 330 yes 502 1 2010 42 0 Existence of $\Psi$-bounded solutions for nonhomogeneous Lyapunov matrix differential equations on $R$
In this paper, we give a necessary and sufficient condition for the existence of at least one $\Psi$-bounded solution of a linear nonhomogeneous Lyapunov matrix differential equation on $\mathbb{R}$. In addition, we give a result in connection with the asymptotic behavior of the $\Psi$-bounded solution of this equation.
 1 9 79 . .
2010-08-24 2010-04-02 1389 yes 503 1 2010 43 0 Oscillation of third-order functional differential equations
The aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear delay differential equation
\begin{equation*}\label{E0}
\left[a(t)\left[x''(t)\right]^{\gamma}\right]'+q(t)f(x\left[\tau(t)\right])=0.
\tag{$E$}
\end{equation*}
Applying suitable comparison theorems we present new criteria for oscillation or certain asymptotic behavior of nonoscillatory solutions of {(\ref{E0})}. Obtained results essentially improve and complement earlier ones. Various examples are considered to illustrate the main results.
 1 10 7 . .
2010-08-24 2010-05-20 584 yes 585 no 504 1 2010 44 0 On multiple sign-changing solutions for some second-order integral boundary value problems
In this paper, by employing fixed point index theory and Leray-Schauder degree theory, we obtain the existence and multiplicity of sign-changing solutions for nonlinear second-order differential equations with integral boundary value conditions.
 1 15 414 . .
2010-08-25 2010-01-15 586 yes 587 no 505 1 2010 45 0 Non-simultaneous blow-up for a reaction-diffusion system with absorption and coupled boundary flux
This paper deals with non-simultaneous blow-up for a reaction-diffusion system with absorption and nonlinear boundary flux. We establish necessary and sufficient conditions for the occurrence of non-simultaneous blow-up with proper initial data.
 1 10 929 . .
2010-08-25 2010-06-10 1410 yes 589 no 506 1 2010 46 0 Periodic solutions of differential equations with a general piecewise constant argument and applications
In this paper we investigate the existence of the periodic solutions of a quasilinear differential equation with piecewise constant argument of generalized type. By using some fixed point theorems and some new analysis technique, sufficient conditions are obtained for the existence and uniqueness of periodic solutions of these systems. A new Gronwall type lemma is proved. Some examples concerning biological models as Lasota-Wazewska, Nicholson's blowflies and logistic models are treated.
 1 19 857 . .
2010-08-26 2010-07-07 590 yes 468 no 507 1 2010 47 0 Global existence and controllability to a stochastic integro-differential equation
In this paper, we are focused upon the global uniqueness results for a stochastic integro-differential equation in Fréchet spaces. The main results are proved by using the resolvent operators combined with a nonlinear alternative of Leray-Schauder type in Fréchet spaces due to Frigon and Granas. As an application, a controllability result with one parameter is given to illustrate the theory.
 1 15 71 . .
2010-08-26 2010-04-27 591 yes 592 no 593 no 508 1 2010 48 0 Oscillatory behaviour of a class of nonlinear second order mixed difference equations
In this paper oscillatory and asymptotic behaviour of solutions of a class of nonlinear second order neutral difference equations with positive and negative coefficients of the form
(E) $ \Delta (r(n) \Delta (y(n) + p(n) y(n-m))) + f(n) H_1(y(n-k_1))-g(n) H_2 (y(n-k_2)) = q(n) $ \\ and
$ \Delta (r(n) \Delta (y(n) + p(n) y(n-m))) + f(n) H_1(y(n-k_1))-g(n) H_2 (y(n-k_2)) = 0 $ \\ \\
are studied under the assumptions
\begin{eqnarray}\sum\limits_{n=0}^{\infty} \frac{1}{r(n)} < \infty \nonumber \end{eqnarray} and
\begin{eqnarray}\sum\limits_{n=0}^{\infty} \frac{1}{r(n)} = \infty \nonumber \end{eqnarray} for various ranges of $p(n)$. Using discrete Krasnoselskii's fixed point theorem sufficient conditions are obtained for existence of positive bounded solutions of (E).
 1 19 7 . .
2010-08-28 2009-10-23 357 yes 509 1 2010 49 0 Oscillation and nonoscillation of two terms linear and half-linear equations of higher order
In this paper we investigate the properties of nonoscillation for the equation $$(-1)^{n}(\rho(t)|y^{(n)}|^{p-2}y^{(n)})^{(n)}-v(t)|y|^{p-2}y=0,$$ where $1<p<\infty$ and ${v}$ is a non-negative continuous function and ${\rho}$ is a positive $n$-times continuously differentiable function on the half-line $[0,\infty)$. When the principle of reciprocity is used for the linear equation ($p=2$) we suppose that the functions ${v}$ and ${\rho}$ are positive and $n$-times continuously differentiable on the half-line $[0,\infty)$.
 1 15 7 . .
2010-09-01 2010-04-02 594 yes 595 no 510 1 2010 50 0 Floquet boundary value problem of fractional functional differential equations
In this paper, we prove the existence of positive solutions for Floquet boundary value problem concerning fractional functional differential equations with bounded delay. The results are obtained by using two fixed point theorems on appropriate cones.
 1 13 71 . .
2010-09-03 2010-02-26 596 yes 598 no 597 no 511 1 2010 51 0 Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition
In this paper, we consider a semilinear parabolic equation
$$u_t=\Delta u+u^q\int_0^tu^p(x,s)ds,\quad x\in \Omega,\quad t>0$$
with nonlocal nonlinear boundary condition $u|_{\partial\Omega\times(0,+\infty)}=\int_\Omeg\varphi(x,y) u^l(y,t)dy$ and nonnegative initial data, where $p$, $q\geq 0$ and $l>0$. The blow-up criteria and the blow-up rate are obtained.
 1 17 414 . .
2010-09-03 2010-04-22 599 yes 589 no 512 1 2010 52 0 Existence of time periodic solutions for one-dimensional Newtonian filtration equation with multiple delays
In this paper, we study one-dimensional Newtonian filtration equation including unbounded sources with multiple delays. The existence of nonnegative non-trivial time periodic solutions will be established by the Leray-Schauder fixed point theorem based on some suitable Lyapunov functionals and some a priori estimates for all possible periodic solutions.
 1 20 107 . .
2010-09-06 2010-03-05 600 yes 134 no 601 no 513 1 2010 53 0 Positive solutions of the $(n-1,1)$ conjugate boundary value problem
We consider the $(n-1,1)$ conjugate boundary value problem. Some upper estimates to positive solutions for the problem are obtained. We also establish some explicit sufficient conditions for the existence and nonexistence of positive solutions of the problem.
 1 13 7 . .
2010-09-10 2010-06-24 241 yes 514 1 2010 54 0 Weak solutions for nonlinear fractional differential equations on reflexive Banach spaces
The aim of this paper is to investigate a class of boundary value problem for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
 1 10 107 . .
2010-09-10 2010-08-25 71 yes 7 no 603 no 515 1 2010 55 0 Multiple solutions for fourth order $m$-point boundary value problems with sign-changing nonlinearity
Using a fixed point theorem in ordered Banach spaces with lattice structure founded by Liu and Sun, this paper investigates the multiplicity of nontrivial solutions for fourth order $m$-point boundary value problems with sign-changing nonlinearity. Our results are new and improve on those in the literature.
 1 10 7 . .
2010-09-15 2009-12-22 605 yes 606 no 516 1 2010 56 0 Existence and uniqueness of positive solutions for a third-order three-point problem on time scales
In this paper, a class of third-order three-point boundary value problem on time scales is considered. Using monotone iterative technique and cone expansion and compression fixed point theorem of norm type, we do not only obtain the existence and uniqueness of positive solutions of the problem, but also establish the iterative schemes for approximating the solutions.
 1 12 7 . .
2010-09-17 2010-07-01 607 yes 517 1 2010 57 0 Note on multiplicative perturbation of local $C$-regularized cosine functions with nondensely defined generators
In this note, we obtain a new multiplicative perturbation theorem for local $C$-regularized cosine function with a nondensely defined generator $A$. An application to an integrodifferential equation is given.
 1 12 7 . .
2010-09-17 2010-01-26 608 yes 609 no 518 1 2010 58 0 On the existence of mild solutions to some semilinear fractional integro-differential equations
This paper deals with the existence of a mild solution for some fractional semilinear differential equations with non local conditions. Using a more appropriate definition of a mild solution than the one given in [12], we prove the existence and uniqueness of such solutions, assuming that the linear part is the infinitesimal generator of an analytic semigroup that is compact for $t > 0$ and the nonlinear part is a Lipschitz continuous function with respect to the norm of a certain interpolation space. An example is provided.
 1 17 71 . .
2010-09-23 2010-05-19 947 yes 610 no 378 no 519 1 2010 59 0 Oscillation of solutions to a higher-order neutral PDE with distributed deviating arguments
This article presents conditions for the oscillation of solutions to neutral partial differential equations. The order of these equations can be even or odd, and the deviating arguments can be distributed over an interval. We also extend our results to a nonlinear equation and to a system of equations.
 1 14 304 . .
2010-09-23 2010-07-15 370 yes 520 1 2010 60 0 Fractal analysis of Hopf bifurcation for a class of completely integrable nonlinear Schrödinger Cauchy problems
We study the complexity of solutions for a class of completely integrable, nonlinear integro-differential Schrödinger initial-boundary value problems on a bounded domain, depending on a real bifurcation parameter. The considered Schrödinger problem is a natural extension of the classical Hopf bifurcation model for planar systems into an infinite-dimensional phase space. Namely, the change in the sign of the bifurcation parameter has a consequence that an attracting (or repelling) invariant subset of the sphere in $L^2(\Omega)$ is born. We measure the complexity of trajectories near the origin by considering the Minkowski content and the box dimension of their finite-dimensional projections. Moreover we consider the compactness and rectifiability of trajectories, and box dimension of multiple spirals and spiral chirps. Finally, we are able to obtain the box dimension of trajectories of some nonintegrable Schrödinger evolution problems using their reformulation in terms of the corresponding (not explicitly solvable) dynamical systems in $\Rb^n$.
 1 32 14 . .
2010-09-24 2010-04-01 611 yes 103 no 612 no 521 1 2010 61 0 Oscillation criteria of second order neutral delay dynamic equations with distributed deviating arguments
In this paper we establish some oscillation theorems for second order neutral dynamic equations with distributed deviating arguments. We use the Riccati transformation technique to obtain sufficient conditions for the oscillation of all solutions. Further, some examples are provided to illustrate the results.
 1 15 107 . .
2010-09-30 2010-02-01 244 yes 613 no 523 1 2010 62 0 On the step-type contrast structure of a second-order semilinear differential equation with integral boundary conditions
In this paper we investigate the step-type contrast structure of a second-order semilinear differential equation with integral boundary conditions. The asymptotic solution is constructed by the boundary function method, and the uniform validity of the formal solution is proved by the theory of differential equalities.
 1 14 79 . .
2010-10-01 2010-07-14 617 yes 618 no 619 no 522 1 2010 63 0 Bifurcation analysis of Rössler system with multiple delayed feedback
In this paper, regarding the delay as parameter, we investigate the effect of delay on the dynamics of a Rössler system with multiple delayed feedback proposed by Ghosh and Chowdhury. At first we consider the stability of equilibrium and the existence of Hopf bifurcations. Then an explicit algorithm for determining the direction and the stability of the bifurcating periodic solutions is derived by using the normal form theory and center manifold argument. Finally, we give a numerical simulation example which indicates that chaotic oscillation is converted into a stable steady state or a stable periodic orbit when the delay passes through certain critical values.
 1 22 25 . .
2010-10-01 2010-02-10 616 yes 615 no 614 no 524 1 2010 64 0 On a class of functional differential equations in Banach spaces
The aim of this paper is to establish the existence of solutions and some properties of set solutions for a Cauchy problem with causal operator in a separable Banach space.
 1 17 304 . .
2010-10-15 2010-08-20 546 yes 525 1 2010 65 0 Existence of solutions for $p(x)$-Laplacian equations
We discuss the problem
\begin{equation*}
\left\{
\begin{array}{ll}
-\func{div}\left( \left\vert \nabla u\right\vert ^{p(x)-2}\nabla u\right)
=\lambda (a\left( x\right) \left\vert u\right\vert ^{q(x)-2}u+b(x)\left\vert u\right\vert ^{h(x)-2}u)\text{,} & \text{for }x\in \Omega , \\ u=0\text{,} & \text{for }x\in \partial \Omega .
\end{array}
\right.
\end{equation*}
where $\Omega $ is a bounded domain with smooth boundary in $\mathbb{R}^{N}$ $\left( N\geq 2\right)$ and $p$ is Lipschitz continuous, $q$ and $h$ are continuous functions on $\overline{\Omega }$ such that $1<q(x)<p(x)<h(x)<p^{\ast }(x)$ and $p(x)<N$. We show the existence of at least one nontrivial weak solution. Our approach relies on the variable exponent theory of Lebesgue and Sobolev spaces combined with adequate variational methods and the Mountain Pass Theorem.
 1 13 107 . .
2010-11-02 2010-01-27 620 yes 621 no 622 no 526 1 2010 66 0 Generalized quasilinearization method for nonlinear boundary value problems with integral boundary conditions
The quasilinearization method coupled with the method of upper and lower solutions is used for a class of nonlinear boundary value problems with integral boundary conditions. We obtain some less restrictive sufficient conditions under which corresponding monotone sequences converge uniformly and quadratically to the unique solution of the problem. An example is also included to illustrate the main result.
 1 14 107 . .
2010-11-02 2010-03-09 624 yes 625 no 623 no 527 1 2010 67 0 On the oscillatory behavior for a certain class of third order nonlinear delay difference equations
By employing the generalized Riccati transformation technique, we will establish some new oscillation criteria for a certain class of third order nonlinear delay difference equations. Our results extend and improve some previously obtained ones. An example is worked out to demonstrate the validity of the proposed results.
 1 16 7 . .
2010-11-05 2010-05-02 121 yes 626 no 627 no 528 1 2010 68 0 Oscillation results on meromorphic solutions of second order differential equations in the complex plane
The main purpose of this paper is to consider the oscillation theory on meromorphic solutions of second order linear differential equations of the form $f^{''}+A(z)f=0$ where $A$ is meromorphic in the complex plane. We improve and extend some oscillation results due to Bank and Laine, Kinnunen, Liang and Liu, and others.
 1 13 107 . .
2010-11-05 2010-04-14 526 yes 629 no 529 1 2010 69 0 A system of degree four with an invariant triangle and at least three small amplitude limit cycles
We show the existence of a polynomial system of degree four having three real invariant straight lines forming a triangle with at least three small amplitude limit cycles in the interior. Also, we obtain the necessary and sufficient conditions for the critical point at the interior of the bounded region to be a center.
 1 7 124 . .
2010-11-18 2009-10-29 630 yes 632 no 631 no 530 1 2010 70 0 Nontrivial solutions for fractional $q$-difference boundary value problems
In this paper, we investigate the existence of nontrivial solutions to the nonlinear $q$-fractional boundary value problem
\begin{align*}
&(D_q^\alpha y)(x)=-f(x,y(x)),\quad 0<x<1,\\
&y(0)=0=y(1),
\end{align*}
by applying a fixed point theorem in cones.
 1 10 107 . .
2010-11-25 2010-08-04 633 yes 531 1 2010 71 0 Some existence results for boundary value problems of fractional differential inclusions with non-separated boundary conditions
In this paper, we study the existence of solutions for a boundary value problem of differential inclusions of order $q \in (1,2]$ with non-separated boundary conditions involving convex and non-convex multivalued maps. Our results are based on the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.
 1 17 7 . .
2010-12-06 2010-08-25 307 yes 70 no 532 1 2010 72 0 Existence of homoclinic orbit for second-order nonlinear difference equation
By using the Mountain Pass Theorem, we establish some existence criteria to guarantee the second-order nonlinear difference equation $\Delta \left[p(t)\Delta u(t-1)\right] +f(t,u(t))=0$ has at least one homoclinic orbit, where $t\in \Z,\ u\in \R$.
 1 14 79 . .
2010-12-13 2010-03-16 634 yes 635 no 533 1 2010 73 0 Note on an anisotropic p-Laplacian equation in $R^n$
In this paper, we study a kind of anisotropic p-Laplacian equations in $R^n$. Nontrivial solutions are obtained using mountain pass theorem given by Ambrosetti-Rabinowitz.
 1 9 19 . .
2010-12-17 2010-10-12 430 yes 534 1 2010 74 0 Existence of positive solutions for a class of higher-order $m$-point boundary value problems
We investigate the existence of positive solutions with respect to a cone for a higher-order nonlinear differential system, subject to some boundary conditions which involve $m$ points.
 1 15 7 . .
2010-12-25 2010-09-05 1901 yes 535 1 2010 75 0 A note on a linear spectral theorem for a class of first order systems in $R^{2N}$
Along the lines of Atkinson, a spectral theorem is proved for the boundary value problem
$$
\left\{\begin{array}{l}
Jz' + f(t) J z + P(t) z= \lambda B(t) z \\
x(0) = x(T) =0, \\
\end{array}\right.
t \in [0, T], z=(x, y) \in \mathbb{R}^N \times \mathbb{R}^N,
$$
where $f(t)$ is real-valued and $P(t), B(t)$ are symmetric matrices, with $B(t)$ positive definite. A suitable rotation index associated to the system is used to highlight the connections between the eigenvalues and the nodal properties of the corresponding eigenfunctions.
 1 22 24 . .
2010-12-25 2010-10-05 639 yes 640 no 536 1 2010 76 0 Existence and uniqueness of positive solutions for Neumann problems of second order impulsive differential equations
This work is concerned with the existence and uniqueness of positive solutions for Neumann boundary value problems of second order impulsive differential equations. The result is obtained by using a fixed point theorem of generalized concave operators.
 1 9 70 . .
2010-12-26 2010-07-15 1019 yes 642 no 537 1 2010 77 0 Positive solutions for singular Sturm-Liouville boundary value problems with integral boundary conditions
In this paper, we study the second-order nonlinear singular Sturm-Liouville boundary value problems with Riemann-Stieltjes integral boundary conditions
\begin{equation*}\begin{cases}
-(p(t)u'(t))'+q(t)u(t)=f(t,u(t)),\; 0<t<1,\\
\alpha_{1}u(0)-\beta_{1}u'(0)=\int_{0}^{1}u(\tau)\mathrm{d}\alpha(\tau),\\
\alpha_{2}u(1)+\beta_{2}u'(1)=\int_{0}^{1}u(\tau)\mathrm{d}\beta(\tau),
\end{cases}\end{equation*}
where $f(t,u)$ is allowed to be singular at $t=0,1$ and $u=0$. Some new results for the existence of positive solutions of the boundary value problems are obtained. Our results extend some known results from the nonsingular case to the singular case, and we also improve and extend some results of the singular cases.
 1 15 414 . .
2010-12-27 2010-07-22 333 yes 643 no 644 no 538 1 2010 78 0 On a nonlinear fractional order differential inclusion
The existence of solutions for a nonlinear fractional order differential inclusion is investigated. Several results are obtained by using suitable fixed point theorems when the right hand side has convex or non convex values.
 1 13 107 . .
2010-12-28 2010-09-14 317 yes 539 1 2010 79 0 The existence of positive solutions for nonlinear boundary system with $p$-Laplacian operator based on sign-changing nonlinearities
In this paper, we study a nonlinear boundary value system with $p$-Laplacian operator
$$\left\{\begin{array}{lll}
(\phi_{p_1}(u'))'+a_1(t)f(u,v)=0, 0<t<1,\cr
(\phi_{p_2}(v'))'+a_2(t)g(u,v)=0, 0<t<1,\cr
\alpha_1\phi_{p_1}(u(0))-\beta_1\phi_{p_1}(u'(0))=\gamma_1\phi_{p_1}(u(1))+\delta_1\phi_{p_1}(u'(1))=0,
\alpha_2\phi_{p_2}(v(0))-\beta_2\phi_{p_2}(v'(0))=\gamma_2\phi_{p_2}(v(1))+\delta_2\phi_{p_2}(v'(1))=0,
\end{array}\right.$$
where $\phi_{p_i}(s)=|s|^{p_i-2}s, p_i>1, i=1,2$. We obtain some sufficient conditions for the existence of two positive solutions or infinitely many positive solutions by using a fixed-point theorem in cones. Especially, the nonlinear terms $f,g $ are allowed to change sign. The conclusions essentially extend and improve the known results.
 1 14 107 . .
2010-12-31 2010-03-11 556 yes 540 1 2011 1 0 Positive solutions for higher-order nonlinear fractional differential equation with integral boundary condition
In this paper, we study a kind of higher-order nonlinear fractional differential equation with integral boundary
condition. The fractional differential operator here is the Caputo's fractional derivative. By means of fixed point theorems, the existence and multiplicity results of positive solutions are obtained. Furthermore, some examples given here illustrate that the results are almost sharp.
 1 15 304 . .
2011-01-07 2010-09-17 433 yes 865 no 541 1 2011 2 0 Positive solutions for three-point nonlinear fractional boundary value problems
In this paper, we give sufficient conditions for the existence or the nonexistence of positive solutions of the nonlinear fractional boundary value problem
\begin{gather*}
D_{0^{+}}^{\alpha}u+a(t)f(u(t))=0, 0<t<1, 2<\alpha<3,\\
u(0)=u^{\prime}(0)=0, u^{\prime}(1)-\mu u^{\prime}(\eta)=\lambda,
\end{gather*}
where $D_{0^{+}}^{\alpha}$ is the standard Riemann-Liouville fractional differential operator of order $\alpha$, $\eta\in\left(0,1\right)$, $\mu\in\left[0,\dfrac{1}{\eta^{\alpha-2}}\right)$ are two arbitrary constants and $\lambda\in\left[ 0,\infty\right) $ is a parameter. The proof uses the Guo-Krasnosel'skii fixed point theorem and Schauder's fixed point theorem.
 1 19 71 . .
2011-01-07 2010-01-24 636 yes 637 no 542 1 2011 3 0 Periodic boundary value problems for nonlinear impulsive fractional differential equation
In this paper, we investigate the existence and uniqueness of solution of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann-Liouville fractional derivative by using Banach contraction principle.
 1 15 70 . .
2011-01-07 2010-09-05 646 yes 351 no 578 1 2011 4 0 Positive solutions for a system of $n$th-order nonlinear boundary value problems
In this paper, we investigate the existence, multiplicity and uniqueness of positive solutions for the following system of $n$th-order nonlinear boundary value problems
\[\begin{cases}
u^{(n)}(t)+f(t,u(t),v(t))=0,0<t<1,\\v^{(n)}(t)+g(t,u(t),v(t))=0, 0<t<1,\\
u(0)=u'(0)=\ldots=u^{(n-2)}(0)=u(1)=0,\\
v(0)= v'(0)=\ldots=v^{(n-2)}(0)=v(1)=0.
\end{cases}\]
Based on a priori estimates achieved by using Jensen's integral inequality, we use fixed point index theory to establish our main results. Our assumptions on the nonlinearities are mostly formulated in terms of spectral radii of associated linear integral operators. In addition, concave and convex functions are utilized to characterize coupling behaviors of $f$ and $g$, so that we can treat the three cases: the first with both superlinear, the second with both sublinear, and the last with one superlinear and the other sublinear.
 1 16 7 . .
2011-02-04 2010-07-23 1131 yes 686 no 574 1 2011 5 0 On the fixed point theorem of Krasnoselskii and Sobolev
We formulate a version of the fixed point theorem of Krasnoselskii and Sobolev in locally convex spaces. We apply this result to establish the existence of solutions of an integral equation defined in an abstract space.
 1 6 71 . .
2011-02-05 2010-10-26 681 yes 445 no 568 1 2011 6 0 Existence of minimal and maximal solutions for a quasilinear elliptic equation with integral boundary conditions
This work is concerned with the construction of the minimal and maximal solutions for a quasilinear elliptic equation with integral boundary conditions, where the nonlinearity is a continuous function depending on the first derivative of the unknown function. We also give an example to illustrate our results.
 1 18 7 . .
2011-02-05 2010-07-09 676 yes 580 1 2011 7 0 Existence of solutions for nonlinear fractional differential equations with impulses and anti-periodic boundary conditions
In this paper, we prove the existence of solutions for an anti-periodic boundary value problem of nonlinear impulsive fractional differential equations by applying some known fixed point theorems. Some examples are presented to illustrate the main results.
 1 11 70 . .
2011-02-07 2010-08-26 688 yes 689 no 558 1 2011 8 0 Properties of the Lindemann mechanism in phase space
We study the planar and scalar reductions of the nonlinear Lindemann mechanism of unimolecular decay. First, we establish that the origin, a degenerate critical point, is globally asymptotically stable. Second, we prove there is a unique scalar solution (the slow manifold) between the horizontal and vertical isoclines. Third, we determine the concavity of all scalar solutions in the nonnegative quadrant. Fourth, we establish that each scalar solution is a centre manifold at the origin given by a Taylor series. Moreover, we develop the leading-order behaviour of all planar solutions as time tends to infinity. Finally, we determine the asymptotic behaviour of the slow manifold at infinity by showing that it is a unique centre manifold for a fixed point at infinity.
 1 31 25 . .
2011-02-07 2010-05-08 667 yes 668 no 586 1 2011 9 0 Infinitely many nontrivial solutions for a class of biharmonic equations via variant fountain theorems
In this paper, we investigate the existence of infinitely many solutions for a class of biharmonic equations where the nonlinearity involves a combination of superlinear and asymptotically linear terms. The solutions are obtained from a variant version of Fountain Theorem.
 1 14 16 . .
2011-02-12 2010-12-14 695 yes 588 1 2011 10 0 Time periodic solutions for a viscous diffusion equation with nonlinear periodic sources
In this paper, we prove the existence of nontrivial nonnegative classical time periodic solutions to the viscous diffusion equation with strongly nonlinear periodic sources. Moreover, we also discuss the asymptotic behavior of solutions as the viscous coefficient $k$ tends to zero.
 1 19 304 . .
2011-02-12 2010-09-08 294 yes 2625 no 134 no 189 no 589 1 2011 11 0 Some results on impulsive boundary value problem for fractional differential inclusions
This paper deals with impulsive fractional differential inclusions with a fractional order multi-point boundary condition and with fractional order impulses. By use of multi-valued analysis and topological fixed point theory, we present some existence results under both convexity and nonconvexity conditions on the multi-valued right-hand side. The compactness of the solutions set and continuous version of Filippov's theorem are also investigated.
 1 24 7 . .
2011-02-12 2010-11-22 697 yes 1498 no 590 1 2011 12 0 Anti-periodic solutions for a class of fourth-order nonlinear differential equations with variable coefficients
By applying the method of coincidence degree, some criteria are established for the existence of anti-periodic solutions for a class of fourth-order nonlinear differential equations with variable coefficients. Finally, an example is given to illustrate our result.
 1 10 71 . .
2011-02-14 2010-01-02 2240 yes 159 no 562 1 2011 13 0 Multiple positive solutions for (n-1, 1)-type semipositone conjugate boundary value problems for coupled systems of nonlinear fractional differential equations
In this paper, we consider (n-1, 1)-type conjugate boundary value problem for coupled systems of the nonlinear fractional differential equation
\begin{gather*}\left\{\begin{array}{ll}
\mathbf{D}_{0+}^\alpha u+\lambda f(t,v)=0, 0<t<1, \lambda >0,\\
\mathbf{D}_{0+}^\alpha v+\lambda g(t,u)=0,\\
u^{(i)}(0)=v^{(i)}(0)=0, 0\leq i\leq n-2,\\
u(1)=v(1)=0,
\end{array}\right.\end{gather*}
where $\lambda$ is a parameter, $\alpha\in(n-1, n]$ is a real number and $n\geq 3$, and $\mathbf{D}_{0+}^\alpha$ is the Riemann-Liouville's fractional derivative, and $f, g$ are continuous and semipositone. We give properties of Green's function of the boundary value problem, and derive an interval on $\lambda$ such that for any $\lambda$ lying in this interval, the semipositone boundary value problem has multiple positive solutions.
 1 12 7 . .
2011-02-16 2010-10-20 574 yes 570 1 2011 14 0 Upper and lower solutions for BVPs on the half-line with variable coefficient and derivative depending nonlinearity
This paper is concerned with a second-order nonlinear boundary value problem with a derivative depending nonlinearity and posed on the positive half-line. The derivative operator is time dependent. Upon a priori estimates and under a Nagumo growth condition, the Schauder's fixed point theorem combined with the method of upper and lower solutions on unbounded domains are used to prove existence of solutions. A uniqueness theorem is also obtained and some examples of application illustrate the obtained results.
 1 18 71 . .
2011-02-28 2010-09-05 1008 yes 677 no 582 1 2011 15 0 On the Dirichlet problem for a Duffing type equation
We use direct variational method in order to investigate the dependence on parameter for the solution for a Duffing type equation with Dirichlet boundary value conditions.
 1 12 71 . .
2011-03-02 2010-01-14 690 yes 557 1 2011 16 0 Connections between the stability of a Poincare map and boundedness of certain associate sequences
Let $m\ge 1$ and $N\ge 2$ be two natural numbers and let ${\mathcal{U}}=\{U(p, q)\}_{p\ge q\ge 0}$ be the $N$-periodic discrete evolution family of $m\times m$ matrices, having complex scalars as entries, generated by ${\mathcal{L}}(\mathbb{C}^m)$-valued, $N$-periodic sequence of $m\times m$ matrices $(A_n).$ We prove that the solution of the following discrete problem $$y_{n+1}=A_ny_n+e^{i\mu n}b,\quad n\in\mathbb{Z}_+,\quad y_0=0$$ is bounded for each $\mu\in\mathbb{R}$ and each $m$-vector $b$ if the Poincare map $U(N, 0)$ is stable. The converse statement is also true if we add a new assumption to the boundedness condition. This new assumption refers to the invertibility for each $\mu\in\mathbb{R}$ of the matrix $V_{\mu}:=\sum\nolimits_{\nu=1}^NU(N, \nu)e^{i\mu \nu}.$ By an example it is shown that the assumption on invertibility cannot be removed. Finally, a strong variant of Barbashin's type theorem is proved.
 1 12 71 . .
2011-03-03 2010-12-03 665 yes 901 no 666 no 457 no 555 1 2011 17 0 Multiple solutions for nonhomogeneous Neumann differential inclusion problems by the p(x)-Laplacian
In this paper we study Neumann-type $p(x)$-Laplacian equation with nonsmooth potential. Firstly, applying a version of the non-smooth three-critical-points theorem we obtain the existence of three solutions of the problem in $W^{1,p(x)}(\Omega)$. Finally, we obtain the existence of at least two nontrivial solutions, when $\alpha^->p^+$.
 1 10 107 . .
2011-03-05 2010-12-14 662 yes 663 no 641 1 2011 18 0 Infinite number of stable periodic solutions for an equation with negative feedback
For all $\mu>0$, a locally Lipschitz continuous map $f$ with $xf\left(x\right)>0$, $x\in\mathbb{R}\setminus\left\{ 0\right\} $, is constructed, such that the scalar equation $\dot{x}\left(t\right)=-\mu x\left(t\right)-f\left(x\left(t-1\right)\right)$ with delayed negative feedback has an infinite number of periodic orbits. All periodic solutions defining these orbits oscillate slowly around $0$ in the sense that they admit at most one sign change in each interval of length of $1$. Moreover, if $f$ is continuously differentiable, then the periodic orbits are hyperbolic and stable. In this example $f$ is not bounded, but the Lipschitz constants for the restrictions of $f$ to certain intervals are small. Based on this property, an infinite sequence of contracting return maps is given. Their fixed points are the initial segments of the periodic solutions.
 1 20 22 . .
2011-03-05 2010-11-16 775 yes 571 1 2011 19 0 Necessary and sufficient conditions for the oscillation of higher-order differential equations involving distributed delays
In this article, we establish necessary and sufficient conditions for the oscillation of both bounded and unbounded solutions of the differential equation
\begin{equation}
\bigg[x(t)+\int_{0}^{\lambda}p(t,v)x(\tau(t,v))\,\mathrm{d}v\bigg]^{(n)}+\int_{0}^{\lambda}q(t,v)x(\sigma(t,v))\,\mathrm{d}v=\varphi(t)\quad\text{for}\t \geq t_{0},\notag
\end{equation}
where $n\in\mathbb{N}$, $t_{0},\lambda\in\mathbb{R}^{+}$, $p\in C([t_{0},\infty)\times[0,\lambda] \mathbb{R})$, $q\in C([t_{0},\infty)\times[0,\lambda],\mathbb{R}^{+})$, $\tau\in C([t_{0},\infty)\times[0 \lambda],\mathbb{R})$ with $\lim_{t\to\infty}\inf_{v\in[0,\lambda]}\tau(t,v)=\infty$ and $\sup_{v\in[0,\lambda]}\tau(t,v)\leq t$ for all $t\geq t_{0}$, $\sigma\in C([t_{0},\infty)\times[0,\lambda],\mathbb{R})$ with $\lim_{t\to\infty}\inf_{v\in[0,\lambda]}\sigma(t,v)=\infty$, and $\varphi\in C([t_{0},\infty),\mathbb{R})$. We also give illustrating examples to show the applicability of these results.
 1 15 304 . .
2011-03-12 2010-07-22 370 yes 455 no 373 no 564 1 2011 20 0 Attractors and basins of dynamical systems
There are several programs for studying dynamical systems, but none of them is very useful for investigating basins and attractors of higher dimensional systems. Our goal in this paper is to show a new algorithm for finding even chaotic attractors and their basins for these systems. We present an implementation and examples for the use of this program.
 1 11 858 . .
2011-03-14 2010-06-03 383 yes 3 no 573 1 2011 21 0 Fully nonlinear boundary value problems with impulse
An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression - expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth as $t\rightarrow\infty$ or $t\rightarrow 0^+$. The nonlinear impulse terms and the nonlinear boundary terms are assumed to satisfy the analogous asymptotic behavior.
 1 11 7 . boundary value problem with impulse, nonlinear boundary condition, compression - expansion fixed point theorem
2011-04-04 2011-01-10 107 yes 680 no 585 1 2011 22 0 A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order
This paper studies a nonlinear fractional differential equation of an arbitrary order with four-point nonlocal integral boundary conditions. Some existence results are obtained by applying standard fixed point theorems and Leray-Schauder degree theory. The involvement of nonlocal parameters in four-point integral boundary conditions of the problem makes the present work distinguished from the available literature on four-point integral boundary value problems which mainly deals with the four-point boundary conditions restrictions on the solution or gradient of the solution of the problem. These integral conditions may be regarded as strip conditions involving segments of arbitrary length of the given interval. Some illustrative examples are presented.
 1 15 71 26A33, 34A12, 34A40 fractional differential equations, four-point integral boundary conditions, existence, fixed point theorem, Leray-Schauder degree
2011-04-06 2011-02-08 307 yes 70 no 607 1 2011 23 0 On the zeros of solutions of any order of derivative of second order linear differential equations taking small functions
In this paper, we investigate the hyper-exponent of convergence of zeros of $f^{(j)}(z)-\varphi(z) (j\in N)$, where $f$ is a solution of second or $k(\geq2)$ order linear differential equation, $\varphi(z)\not\equiv0$ is an entire function satisfying $\sigma(\varphi)<\sigma(f)$ or $\sigma_{2}(\varphi)<\sigma_{2}(f)$. We obtain some precise results which improve the previous results in [3, 5] and revise the previous results in [11, 13]. More importantly, these results also provide us a method to investigate the hyper-exponent of convergence of zeros of $f^{(j)}(z)-\varphi(z)(j\in N)$.
 1 17 107 30D35, 34M05 linear differential equations, hyper-order, hyper-exponent of convergence of zeros
2011-04-06 2010-10-11 528 yes 525 no 722 no 626 1 2011 24 0 q-Karamata functions and second order q-difference equations
In this paper we introduce and study $q$-rapidly varying functions on the lattice $q^{N_0}:=\{q^k:k\in N_0\}$, $q>1$, which naturally extend the recently established concept of $q$-regularly varying functions. These types of functions together form the class of the so-called $q$-Karamata functions. The theory of $q$-Karamata functions is then applied to half-linear $q$-difference equations to get information about asymptotic behavior of nonoscillatory solutions. The obtained results can be seen as $q$-versions of the existing ones
in the linear and half-linear differential equation case. However two important aspects need to be emphasized. First, a new method of the proof is presented. This method is designed just for the $q$-calculus case and turns out to be an elegant and powerful tool also for the examination of the asymptotic behavior to many other $q$-difference equations, which then may serve to predict how their (trickily detectable) continuous counterparts look like. Second, our results show that $q^{N_0}$ is a very natural setting for the theory of $q$-rapidly and $q$-regularly varying functions and its applications, and reveal some interesting phenomena, which are not known from the continuous theory.
 1 20 7 26A12, 39A12, 39A13 regularly varying functions, rapidly varying functions, $q$-difference equations, asymptotic behavior
2011-04-06 2010-11-15 1484 yes 756 no 591 1 2011 25 0 Positive almost periodic type solutions to a class of nonlinear difference equation
This paper is concerned with positive almost periodic type solutions to a class of nonlinear difference equation with delay. By using a fixed point theorem in partially ordered Banach spaces, we establish several theorems about the existence and uniqueness of positive almost periodic type solutions to the addressed difference equation. In addition, in order to prove our main results, some basic and important properties about pseudo almost periodic sequences are presented.
 1 17 71 34K14, 39A24 almost periodic, asymptotical almost periodic, pseudo almost periodic, nonlinear difference equation, positive solution
2011-04-06 2011-02-12 700 no 701 no 378 yes 554 1 2011 26 0 Qualitative analysis on a cubic predator-prey system with diffusion
In this paper, we study a cubic predator-prey model with diffusion. We first establish the global stability of the trivial and nontrivial constant steady states for the reaction diffusion system, and then prove the existence and non-existence results concerning non-constant positive stationary solutions by using topological argument and the energy method, respectively.
 1 15 16 . cubic predator-prey model, diffusion, steady-state, existence and non-existence
2011-04-08 2010-01-01 899 yes 677 1 2011 27 0 Existence of solutions for fractional differential equations with multi-point boundary conditions at resonance on a half-line
In this paper, we investigate the existence of solutions for multi-point boundary value problems at resonance concerning fractional differential equation on a half-line. Our analysis relies on the coincidence degree of Mawhin. As an application, an example is presented to illustrate the main results.
 1 16 16 34A08, 34B10, 34B40 Fractional differential equations, multi-point boundary conditions, resonance, coincidence degree theorem, half-line
2011-04-11 2011-02-23 819 no 617 yes 818 no 675 1 2011 28 0 Periodic solutions for a delay model of plankton allelopathy on time scales
In this paper, a delay model of plankton allelopathy is investigated. By using the coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. The presented criteria improve and extend previous results in the literature.
 1 7 16 92D25, 34C25 Periodic solutions, time scale, coincidence degree, plankton allelopathy
2011-04-12 2010-08-24 817 no 816 yes 707 1 2011 29 0 Existence of positive solutions for singular impulsive differential equations with integral boundary conditions on an infinite interval in Banach spaces
In this paper, the Mönch fixed point theorem is used to investigate the existence of positive solutions for the second-order boundary value problem with integral boundary conditions of nonlinear impulsive differential equations on an infinite interval in a Banach space.
 1 18 107 34B15, 34B16, 34B40 impulsive singular differential equations, positive solutions, M\"onch fixed point theorem, measure of non-compactness
2011-04-12 2011-03-11 852 yes 586 no 666 1 2011 30 0 Existence of almost periodic solution for SICNN with a neutral delay
In this paper, a kind of shunting inhibitory cellular neural network with a neutral delay was considered. By using the Banach fixed point theorem, we established a result about the existence and uniqueness of the almost periodic solution for the shunting inhibitory cellular neural network.
 1 12 107 . shunting inhibitory cellular neural network, neutral delay, almost periodic solution, fixed point theorem
2011-04-18 2010-07-01 804 yes 805 no 781 1 2011 31 0 On S-shaped and reversed S-shaped bifurcation curves for singular problems
We analyze the positive solutions to the singular boundary value problem
\begin{equation*}\begin{cases}
-(|u'|^{p-2}u)'=\lambda \frac{g(u)}{u^\beta}; (0,1),\\
u(0)=0=u(1),
\end{cases}\end{equation*}
where $p>1,\beta\in(0,1),\lambda>0$ and $g:[0,\infty) \rightarrow\mathbb{R}$ is a $C^1$ function. In particular, we discuss examples when $g(0)>0$ and when $g(0)<0$ that lead to $S$-shaped and reversed $S$-shaped bifurcation curves, respectively.
 1 12 7 . bifurcation
2011-04-18 2011-01-02 951 yes 952 no 478 no 643 1 2011 32 0 Boundary layer analysis for nonlinear singularly perturbed differential equations
This paper focuses on the boundary layer phenomenon arising in the study of singularly perturbed differential equations. Our tools include the method of lower and upper solutions combined with analysis of the integral equation associated with the class of nonlinear equations under consideration.
 1 11 107 34E15, 34A34, 34A40, 34B10 singularly perturbed systems, three-point boundary value problem, method of lower and upper solutions
2011-04-18 2011-02-01 533 yes 994 no 995 no 618 1 2011 33 0 On Barreira-Valls polynomial stability of evolution operators in Banach spaces
Our main objective is to consider a concept of nonuniform behavior and obtain appropriate versions of the well-known stability due to R. Datko and L. Barbashin. This concept has been considered in the works of L. Barreira and C. Valls. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability.
 1 10 79 . 34D05, 34E05
2011-05-11 2010-10-19 741 no 742 no 743 yes 548 1 2011 34 0 Second-order differential inclusions with almost convex right-hand sides
We study the existence of solutions of a boundary second order differential inclusion under conditions that are strictly weaker than the usual assumption of convexity on the values of the right-hand side.
 1 14 71 34A60, 28A25, 28C20 differential inclusion, almost convex
2011-05-11 2010-12-12 410 yes 654 no 563 1 2011 35 0 Dulac-Cherkas functions for generalized Liénard systems
Dulac-Cherkas functions can be used to derive an upper bound for the number of limit cycles of planar autonomous differential systems including criteria for the non-existence of limit cycles, at the same time they provide information about their stability and hyperbolicity. In this paper, we present a method to construct  a special class of Dulac-Cherkas functions for  generalized Liénard systems of the type $ \frac{dx}{dt} = y, \quad  \frac{dy}{dt} = \sum_{j=0}^l h_j(x) y^j$ with $l \ge 1$. In case $1 \le l \le 3$,  linear differential equations play a key role in this process, for $ l \ge 4$, we have to solve a system of linear differential and algebraic equations, where the number of equations is larger than the number of unknowns. Finally,  we show that Dulac-Cherkas functions can be used to construct generalized Liénard systems with any $l$ possessing limit cycles.
 1 23 866 34C07, 34C05 number of limit cycles, generalized Lienard systems, Dulac-Cherkas functions, systems of linear differential and algebraic equations
2011-06-04 2010-10-08 340 yes 341 no 339 no 780 1 2011 36 0 On the fundamental solution of linear delay differential equations with multiple delays
For a class of linear autonomous delay differential equations with parameter $\alpha$ we give upper bounds for the integral $\int_{0}^{\infty}\left|X\left(t,\alpha\right)\right|\mbox{d}t$ of the fundamental solution $X\left(\cdot,\alpha\right)$. The asymptotic estimations are sharp at a critical value $\alpha_{0}$ where $x=0$ loses stability. We use these results to study the stability properties of perturbed equations.
 1 28 858 34K06, 34K20 linear delay differential equation, fundamental solution, Laplace transform, discrete Lyapunov functional
2011-06-04 2011-04-02 775 yes 124 no 551 1 2011 37 0 Weak solvability of a hyperbolic integro-differential equation with integral condition
By using the method of semidiscretization in time also called the Rothe's method, we prove the existence, uniqueness of the weak solution and its continuous dependence upon data, for an hyperbolic integro-differential equation with initial, Neumann and integral conditions.
 1 16 70 34K20, 35k55, 35A35, 65M20 Rothe's method, hyperbolic equation, integrodifferential equation, weak solution
2011-06-08 2011-01-15 657 no 658 yes 784 1 2011 38 0 Asymptotic stability of two dimensional systems of linear difference equations and of second order half-linear differential equations with step function coefficients
We give a sufficient condition guaranteeing asymptotic stability with respect to $x$ for the zero solution of the half-linear differential equation \[x''|x'|^{n-1} + q(t)|x|^{n-1}x=0, \qquad 1\le n \in \mathbb{R},\] with step function coefficient $q$. The geometric method of the proof can be applied also to two dimensional systems of linear non-autonomous difference equations. The application gives a new simple proof for a sharpened version of \'A. Elbert's asymptotic stability theorems for such difference equations and linear second order differential equations with step function coefficients.
 1 17 3 34D20, 39A30 asymptotic stability, Armellini-Tonelli-Sansone Theorem, step function coefficients, half-linear differential equation
2011-06-08 2011-04-02 948 no 858 yes 679 1 2011 39 0 Fixed points and asymptotic stability of nonlinear fractional difference equations
In this paper, we discuss nonlinear fractional difference equations with the Caputo like difference operator. Some asymptotic stability results of equations under investigated are obtained by employing Schauder fixed point theorem and discrete Arzela-Ascoli's theorem. Three examples are also provided to illustrate our main results.
 1 18 107 26A33, 39A11, 47H10 fractional difference equation, Caputo like difference, asymptotic stability, Schauder fixed point theorem, discrete Arzela-Ascoli's theorem
2011-06-08 2011-02-24 821 yes 561 1 2011 40 0 On the superlinear problem involving the $p(x)$-Laplacian
This paper deals with the superlinear elliptic problem without Ambrosetti and Rabinowitz type growth condition of the form:
\begin{align*}\left\{
\begin{aligned}
&-div(|\nabla u|^{p(x)-2}\nabla u)=\lambda f(x,u) \text{in} \Omega,\\
&u=0 \text{on} \partial \Omega,
\end{aligned}
\right.\end{align*}
where $\Omega\subset R^{N}(N\geq 2)$ is a bounded domain with smooth boundary $\partial \Omega$, $\lambda>0$ is a parameter. Existence of nontrivial solution is established for arbitrary $\lambda>0$. Firstly, by using the mountain pass theorem a nontrivial solution is constructed for almost every parameter $\lambda>0$. Then, it is considered the continuation of the solutions. Our results are a generalization of Miyagaki and Souto.
 1 9 79 35J60, 58E30 superlinear problem, $p(x)$-Laplacian, variational method, variable exponent spaces
2011-06-08 2011-01-16 672 yes 834 1 2011 41 0 Positive periodic solutions of delayed Nicholson's blowflies model with a linear harvesting term
This paper is concerned with a class of Nicholson's blowflies model with a linear harvesting term. By applying the method of coincidence degree, some criteria are established for the existence and uniqueness of positive periodic solutions of the model. Moreover, an example is employed to illustrate the main results.
 1 11 16 34C25, 34K13 Nicholson's blowflies model, positive periodic solutions, coincidence degree, existence and uniqueness, harvesting term
2011-06-08 2011-04-24 1065 yes 1067 no 604 1 2011 42 0 Periodic solutions for a porous medium equation
In this paper, we study with a periodic porous medium equation with nonlinear convection terms and weakly nonlinear sources under Dirichlet boundary conditions. Based on the theory of Leray-Shauder fixed point theorem, we establish the existence of periodic solutions.
 1 7 25 35B10, 35K55, 35K65 existence, periodic solutions, Leray-Schauder fixed point theorem
2011-04-08 2010-06-10 718 no 717 yes 719 no 547 1 2011 43 0 Stability in nonlinear neutral differential equations with variable delays using fixed point theory
The purpose of this paper is to use a fixed point approach to obtain asymptotic stability results of a nonlinear neutral differential equation with variable delays. An asymptotic stability theorem with a necessary and sufficient condition is proved. In our consideration we allow the coefficient functions to change sign and do not require bounded delays. The obtained results improve and generalize those due to Burton, Zhang and Raffoul. We end by giving three examples to illustrate our work.
 1 11 71 34K20, 34K30, 34K40 fixed points, stability, neutral differential equation, integral equation, variable delays
2011-06-14 2011-01-11 652 yes 653 no 662 1 2011 44 0 Forced oscillation of second-order superlinear dynamic equations on time scales
In this paper, by constructing a class of Philos type functions on time scales, we investigate the oscillation of the following second-order forced nonlinear dynamic equation
$$x^{\Delta\Delta}(t)-p(t)|x(q(t))|^{\lambda-1}x(q(t))=e(t),\quad t\in\mathbb{T}$$
where $\mathbb{T}$ is a time scale, $p,e:\mathbb{T}\to\mathbb{R}$ are right dense continuous functions with $p>0$, $\lambda>1$ is a constant, and $q(t)=t$ or $q(t)=\sigma(t)$. Our results not only unify the oscillation of second-order forced differential equations and their discrete analogues, but also complement several results in the literature.
 1 11 107 34N05, 34C10, 39A21 time scales, oscillation, dynamic equations, second-order
2011-06-14 2010-07-03 1390 yes 560 1 2011 45 0 Some remarks on a fractional differential inclusion with non-separated boundary conditions
We study a boundary value problem for a fractional differential inclusion of order $\alpha \in (1,2]$ with with non-separated boundary conditions involving a nonconvex set-valued map. We establish a Filippov type existence theorem and we prove the arcwise connectedness of the solution set of the problem considered.
 1 14 7 34A60, 26A33, 34B15 differential inclusion, fractional derivative, boundary value problem
2011-06-14 2011-01-13 317 yes 797 1 2011 46 0 Step-like contrast structure of singularly perturbed optimal control problem
In this paper, the existence of step-like contrast structure for a class of singularly perturbed optimal control problem is shown by the contrast structure theory. By means of direct scheme of boundary function method, we construct the uniformly valid asymptotic solution for the singularly perturbed optimal control problem. Finally, an example is presented to show the result.
 1 16 107 34B15, 34E15 singular perturbation, optimal control, contrast structure
2011-06-27 2011-04-08 957 yes 619 no 975 no 559 1 2011 47 0 Strictly localized bounding functions and Floquet boundary value problems
Semilinear multivalued equations are considered, in separable Banach spaces with the Radon-Nikodym property. An effective criterion for the existence of solutions to the associated Floquet boundary value problem is showed. Its proof is obtained combining a continuation principle with a Liapunov-like technique and a Scorza-Dragoni type theorem. A strictly localized transversality condition is assumed. The employed method enables to localize the solution values in a not necessarily invariant set; it allows also to introduce nonlinearities with superlinear growth in the state variable.
 1 18 866 34G25, 34B15, 47H04, 47H09 multivalued boundary value problems, differential inclusions in Banach spaces, bound sets, Floquet problems, Scorza-Dragoni type results
2011-07-06 2010-12-06 669 yes 670 no 671 no 647 1 2011 48 0 Linear differential equations with coefficients in Fock type space
In this paper we deal with complex differential equations of the form
\begin{eqnarray*}
f^{(k)}+a_{k-1}(z)f^{(k-1)}+\cdot\cdot\cdot+a_{1}(z)f^{'}+a_{0}(z)f=0
\end{eqnarray*}
with the coefficients in Fock type space. The relation between the solutions and coefficients in Fock type space is obtained.
 1 10 107 34M10, 30D35 linear differential equations, Fock type spaces, entire functions
2011-06-07 2010-11-30 780 yes 528 no 798 1 2011 49 0 A note on the well-posedness of the nonlocal boundary value problem for elliptic-parabolic equations
The abstract nonlocal boundary value problem
\begin{equation*}\left\{\begin{array}{l}
-\frac{d^{2}u(t)}{dt^{2}}+sign(t)Au(t)=g(t),(0\leq t\leq 1), \\
\frac{du(t)}{dt}+sign(t)Au(t)=f(t),(-1\leq t\leq 0), \\
u(1)=u(-1)+\mu
\end{array}\right.\end{equation*}
for the differential equation in a Hilbert space $H$ with the self-adjoint positive definite operator $A$ is considered. The well-posedness of this problem in Hölder spaces without a weight is established. The coercivity inequalities for solutions of the boundary value problem for elliptic-parabolic equations are obtained.
 1 16 11 35M10, 65J10 elliptic-parabolic equation, nonlocal boundary-value problem, well-posedness
2011-07-07 2011-04-08 2609 yes 941 1 2011 50 0 Controllability of nonlocal impulsive stochastic quasilinear integrodifferential systems
Sufficient conditions for controllability of nonlocal impulsive stochastic quasilinear integrodifferential systems in Hilbert spaces are established. The results are obtained by using evolution operator, semigroup theory and fixed point technique. As an application, an example is provided to illustrate the obtained result.
 1 16 79 93B05, 34A37, 34K50 controllability, impulsive stochastic quasilinear integrodifferential systems, fixed point
2011-07-14 2011-06-06 1173 yes 538 no 713 1 2011 51 0 Differentiation of solutions of nonlocal boundary value problems with respect to boundary data
In this paper, we investigate boundary data smoothness for solutions of the nonlocal boundary value problem, $y^{(n)}=f(x,y,y',\ldots,y^{(n-1)}),y^{(i)}(x_j)=y_{ij}$ and $y^{(i)}(x_k)-\ds\sum_{p=1}^m r_{ip}y(\eta_{ip})=y_{ik}.$ Essentially, we show under certain conditions that partial derivatives of the solution to the problem above exist with respect to boundary conditions and solve the associated variational equation. Lastly, we provide a corollary and nontrivial example.
 1 11 107 34B10, 34B15 Nonlinear boundary value problem, variational equation, ordinary differential equation, nonlocal boundary condition, uniqueness, existence
2011-07-15 2011-03-13 860 yes 711 1 2011 52 0 An existence result for fractional differential equations of neutral type with infinite delay
In this paper, the existence of mild solutions for the fractional differential equations of neutral type with infinite delay is obtained under the conditions in respect of the Kuratowski's measure of noncompactness. As an application, the existence of mild solution for some integrodifferential equation is obtained.
 1 15 71 34K05, 47D06 fractional differential equation, neutral differential equation, mild solution, infinite delay, measure of noncompactness
2011-07-15 2011-03-10 608 yes 712 1 2011 53 0 On mild solutions to fractional differential equations with nonlocal conditions
We prove new existence results of mild solutions to fractional differential equations with nonlocal conditions in Banach spaces. The nonlocal item is only assumed to be continuous. This generalizes some recent results in this area.
 1 13 70 34K05, 34A12, 34A40 nonlocal condition, fractional differential equations, strongly continuous semigroup, fixed point theorem
2011-07-15 2011-03-12 855 no 856 yes 764 1 2011 54 0 Uniqueness in some higher order elliptic boundary value problems in n dimensional domains
We develop maximum principles for several P functions which are defined on solutions to equations of fourth and sixth order (including a equation which arises in plate theory and bending of cylindrical shells). As a consequence, we obtain uniqueness results for fourth and sixth order boundary value problems in arbitrary n dimensional domains.
 1 12 414 35B50, 35G15, 35J40 P function method, higher order elliptic, plate theory
2011-07-15 2011-03-27 918 yes 923 1 2011 55 0 Periodic solutions to a $p$-Laplacian neutral Duffing equation with variable parameter
We study a type of $p$-Laplacian neutral Duffing functional differential equation with variable parameter to establish new results on the existence of $T$-periodic solutions. The proof is based on a famous continuation theorem for coincidence degree theory. Our research enriches the contents of neutral equations and generalizes known results. An example is given to illustrate the effectiveness of our results.
 1 18 16 34B15, 34B24, 34B20 variable parameter, neutral, coincidence degree theory
2011-07-18 2011-05-27 1160 yes 1296 no 676 1 2011 56 0 Multiple solutions of nonlocal boundary value problems for fractional differential equations on half-line
In this paper, we study the existence of multiple solutions of nonlocal boundary value problems for fractional differential equations with integral boundary conditions on the half-line. Applying the fixed point theory and the upper and lower solutions method, some new results on the existence of at least three nonnegative solutions are obtained. An example is presented to illustrate the application of our main results.
 1 14 414 34B15, 26A33 fractional differential equations, Caputo derivative, integral boundary condition, lower and upper solutions, half-line
2011-07-20 2011-02-20 333 no 450 yes 601 1 2011 57 0 Triple positive  solutions of nth order impulsive integro-differential equations
In this paper, we prove the existence of at least three positive solutions of boundary value problems for nth order nonlinear impulsive integro-differential equations of mixed type on infinite interval with infinite number of impulsive times. Our results are obtained by applying a new fixed point theorem introduced by Avery and Peterson.
 1 13 7 . impulsive integro-differential equation, cone and partial ordering, positive solution, fixed point 2011-07-25 2008-06-24 380 no 379 yes 770 1 2011 58 0 Existence and approximation of solutions to three-point boundary value problems for fractional differential equations
In this paper, we study existence and approximation of solutions to some three-point boundary value problems for fractional differential equations of the type
\begin{equation*}\begin{split}
{}^{c}\mathcal{D}_{0+}^{q}u(t)+f(t,u(t))&=0, t\in(0,1), 1<q<2\\
u^{'}(0)=0, \xi u(\eta)&=u(1),
\end{split}\end{equation*}
where $\xi, \eta\in(0,1)$ and ${}^{c}\mathcal{D}_{0+}^{q}$ is the fractional derivative in the sense of Caputo. For the existence of solution, we develop the method of upper and lower solutions and for the approximation of solutions, we develop the generalized quasilinearization technique (GQT). The GQT generates a monotone sequence of solutions of linear problems that converges monotonically and quadratically to solution of the original nonlinear problem.
 1 8 71 . boundary value problems, fractional differential equations, three-point boundary conditions, upper and lower solutions, generalized quasilinearization
2011-08-18 2011-03-30 221 yes 867 1 2011 59 0 On the solvability of the periodic problem for systems of linear functional differential equations with regular operators
Systems of two linear functional differential equations of the first order with regular operators are considered. General necessary and sufficient conditions for the unique solvability of the periodic problem are obtained. For one system with monotone operators we get effective necessary and sufficient conditions for the unique solvability of the periodic problem.
 1 17 11 34K06, 34K10, 34K13 periodic problems, functional differential equations, unique solvability
2011-08-18 2011-05-11 1079 yes 1016 1 2011 60 0 Bounds for the sums of zeros of solutions of $u^{(m)}=P(z)u$ where $P$ is a polynomial
The main purpose of this paper is to consider the differential equation $u^{(m)}=P(z)u$ $(m\geq 2)$ where $P$ is a polynomial with in general complex coefficients. Let $z_{k}(u),$ $k=1,2,\ldots$ be the zeros of a nonzero solution $u$ to that equation. We obtain bounds for the sums $$\sum_{k=1}^{j}\frac{1}{|z_{k}(u)|}\quad (j\in\mathbb{N})$$ which extend some recent results proved by Gil'.
 1 10 107 34M05, 34M10, 34C10, 34A30 complex differential equation, zeros of solution, polynomial
2011-08-18 2011-06-28 526 yes 1240 no 525 no 783 1 2011 61 0 Smoothing properties for Hirota-Satsuma systems
We study local existence and smoothing properties for the initial value problem associated to Hirota-Satsuma systems that describes an interaction of two long waves with different dispersion relations.
 1 30 79 35Q53, 47J35 Evolution equations, weighted Sobolev space, gain in regularity
2011-08-18 2011-04-02 961 no 270 yes 800 1 2011 62 0 A necessary and sufficient condition for existence and uniqueness of periodic solutions for a p-Laplacian Liénard equation
In this work, we investigate the following $p$-Laplacian Li\'enard equation:
$$
(\varphi_{p}(x'(t)))'+f(x(t))x'(t)+g(x(t))=e(t).
$$
Under some assumption, a necessary and sufficient condition for the existence and uniqueness of periodic solutions of this equation is given by using Manásevich--Mawhin continuation theorem. Our results improve and extend some known results.
 1 7 7 34C25 periodic solution, $p$-Laplacian, Liénard equation, continuation theorem
2011-08-22 2011-04-08 974 no 973 yes 1315 no 1386 no 1003 1 2011 63 0 Ulam stability and data dependence for fractional differential equations with Caputo derivative
In this paper, Ulam stability and data dependence for fractional differential equations with Caputo fractional derivative of order $\alpha$ are studied. We present four types of Ulam stability results for the fractional differential equation in the case of $0<\alpha<1$ and $b=+\infty$ by virtue of the Henry-Gronwall inequality. Meanwhile, we give an interesting data dependence results for the fractional differential equation in the case of $1<\alpha<2$ and $b<+\infty$ by virtue of a generalized Henry-Gronwall inequality with mixed integral term. Finally, examples are given to illustrate our theory results.
 1 10 79 34G20, 34A40, 45N05, 47H10 fractional differential equations, Caputo derivative, Ulam stability, data dependence, Gronwall inequality
2011-08-23 2011-06-25 418 yes 1158 no 596 no 603 1 2011 64 0 Approximate solutions for fractional differential equation in the unit disk
In this paper we establish the existence solution approximately for differential equation of fractional order takes the form
\[z^{\alpha} D[ D^{\alpha} u(z)] +(b-z)u'(z)-a u(z)=0, \quad a \neq 0, |b|< 1, 0 < \alpha < 1,\]
subject to the initial conditions $u(0)=u_{0}$ and $u'(0)=u_{1},$ in the unit disk $U:= \{z \in \mathbb{C}: |z|<1 \}.$ The uniqueness of this solution is discussed. The general analytic solutions are posed. Moreover, the Hyers-Ulam stability is studied. An example is illustrated.
 1 11 71 34A12 approximate solution, fractional operators, fractional differential equation, unit disk, Hyers-Ulam stability, existence and uniqueness
2011-08-25 2011-01-25 716 yes 776 1 2011 65 0 Existence of almost periodic solutions to some third-order nonautonomous differential equations
In this paper using the well-known Schauder fixed point theorem we study and obtain the existence of almost periodic mild solutions to some classes of nonautonomous third-order differential equations on a separable infinite dimensional complex Hilbert space.
 1 14 71 39A24, 37L05, 34D09 Schauder fixed point theorem, exponential dichotomy, exponentially stable, almost periodic, third-order differential equation
2011-08-25 2011-04-01 947 yes 1079 1 2011 66 0 Existence of solutions of nonlinear fractional differential equations at resonance
In this paper we study the existence of solutions of nonlinear fractional differential equations at resonance. By using the coincidence degree theory due to Mawhin, the existence of solutions is obtained.
 1 12 16 34A08, 34B15 fractional differential equations, boundary value problems, resonance, coincidence degree theory
2011-08-25 2011-07-24 1311 yes 714 1 2011 67 0 Existence and multiplicity of solutions for a Dirichlet problem involving the discrete p(x)-Laplacian operator
In the present paper, using the three critical points theorem and variational method, we study the existence and multiplicity of solutions for a Dirichlet problem involving the discrete p(x)-Laplacian operator.
 1 10 7 47A75, 35B38, 35P30, 34L05, 34L30 discrete boundary value problem, critical point theory, discrete p(x)-Laplacian
2011-08-29 2011-03-14 620 yes 863 no 864 no 826 1 2011 68 0 First-order three-point BVPs at resonance (II)
This paper deals with existence of solutions to three-point BVPs in perturbed systems of first-order ordinary differential equations at resonance. An existence theorem is established by using the Theorem of Borsuk and some examples are given to illustrate it. A result for computing the local degree of polynomials whose terms of highest order have no common real linear factors is also presented.
1 21 414 34B10 three-point boundary value problems, theorem of Borsuk, resonance case
2011-08-28