Absztrakt: | The author considers the nonautonomous system $$x'(t)=F(t,x_t),\
F(t,0)\equiv 0,\tag 1$$ where $C=C([-h,0];\bbfR^n)$ denotes the
space of continuous functions from $[-h,0]$ into $\bbfR^n,\ 0<h=\text{const.}$;
$F:\bbfR_{+}\times C\to\bbfR^n$ is continuous and maps bounded
sets into bounded sets. For any solution $x:[t_0-h,T]\to\bbfR^n$
and any $t\in [t_0,T]$, the segment $x_t\in C$ is defined by
$x_t(s):=x(t+s),\ -h\leq s\leq 0$.\par
The paper is concerned
with conditions of different kinds of stability of the zero solution
to (1). The main tool in the stability investigations is Lyapunov's
direct method.}
\RV{J.Ohriska (Ko\v{s}ice) |