# Hatvani László honlapja

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 Cím: Asymptotic stability of second order ordinary, functional, and partial differential equations. Szerzõ: Burton, T.A.; Hatvani, L. Forrás: J. Math. Anal. Appl. 176, No.1, 261-281 (1993). Nyelv: English Absztrakt: The authors propose a unified treatment of the asymptotic stability for the equations $u''+a(t)u'+u=0$, $u\sb{tt}=u\sb{xx}-a(t)u\sb t$ with $u(t,0)=u(t,\pi)=0$ and $u''+a(t)u'+u(t-r)=0$. Their approach is based on a certain transformation of the considered equations into equivalent systems of two differential equations of first order in time. For these systems, suitable Lyapunov functions are defined and a sufficient condition for asymptotic stability expressed in terms of these functions is given. Several cases in which the given sufficient condition is satisfied are indicated. In this way the authors obtain results which are comparable with some of the best classical ones for ordinary differential equations. Finally, corresponding considerations for nonlinear problems are given.} \RV{C.Popa (Ia\c{s}i) Letöltés: | Zentralblatt