# Hatvani László honlapja

### Publikációs lista

Vissza.

 Cím: On the stability theory for nonautonomous functional differential equations. Szerzõ: 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 Letöltés: | Zentralblatt