| Absztrakt: | [For the entire collection see Zbl 0695.00015.] \par
Nonautonomous
functional differential equation is considered in the general
case when the right-hand side can be unbounded as a function
of time t. Sufficient conditions for the asymptotic stability
and uniform asymptotic stability are given via Lyapunov functionals
provided that the derivative of the Lyapunov functional is estimated
either by $V'(t,x\sb t)\le -\eta (t)W(\vert x(t)\vert)$ or by
$V'(t,x\sb t)\le -\eta (t)W(\vert\vert\vert x\sb t\vert\vert\vert)$
where $\eta$ : $R\sb+\to R\sb+$ is measurable, W: $R\sb+\to R\sb+$
is continuous, strictly increasing with $W(0)=0$, and $\vert\vert\vert
\cdot \vert\vert\vert$ denotes the $L\sb 2$-norm.}
\RV{L.Hatvani |