| 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 |