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Cím:On the stability theory for nonautonomous functional differential equations.
Szerző:Hatvani, L.
Forrás:Nonlinear oscillations, Proc. 11th Int. Conf., Budapest 1987, 413-415 (1987).
Nyelv:English
Absztrakt:[For the entire collection see Zbl 0624.00010.] \par The consequences of the existence of a Lyapunov-Krasovskij functional V satisfying an inequality $V'(t,x\sb t)\le -\eta (t)W(D(t,x\sb t))$ are investigated, where $\eta$ : $R\sb+\to R\sb+$ is measurable, $W: R\sb+\to R\sb+$ is continuous and strictly increasing with $W(0)=0$, D is a nonnegative continuous functional. Under suitable conditions on V, $\eta$, D, the zero solution is uniformly asymptotically stable. The results are applied to the study of the asymptotic behaviour of the solutions of the equation $x''(t)+\phi (x'(t),t)+f(x(t-h(t)))=0,$ where $xf(x)>0$ (x$\ne 0)$ and $\phi$ (y,t)$\ge 0$.} \RV{L.Hatvani 
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