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Cím:Necessary and sufficient conditions for intermittent stabilization of linear oscillators by large damping.
Szerző:Hatvani, L.; Krisztin, T.
Forrás:Differ. Integral Equ. 10, No.2, 265-272 (1997).
Nyelv:English
Absztrakt:Authors' abstract: ``The oscillator $$ x''+h(t)x'+x=0 $$ is considered, where the damping $h\: \bbfR_+\to \bbfR_+$ is piecewise continuous and large in the sense $$\liminf_{t\to \infty } \int _{t}^{t+\delta } h>0\quad \text { for every } \delta >0. $$ The problem of intermittent damping, initiated by P. Pucci and J. Serrin, is investigated. Let a sequence $\{I_n=[\alpha _n, \beta _n]\}$ of disjoint intervals be given such that $\alpha _n\to \infty $ as $n\to \infty$. A necessary and sufficient condition is given for $I_n$ and $h$ on $I:\bigcup _{n=1}^\infty I_n$ guaranteeing $x(t)\to 0$, $x'(t)\to 0,$ as $t\to \infty $ for every solution $x,$ anyway $h$ may be defined out of $I$''.} \RV{J.Andres (Olomouc) 
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