| Absztrakt: | Authors' abstract: ``The oscillator $$ x''+h(t)x'+x=0 $$ is considered,
where the damping $h\: \bbfR_+\to \bbfR_+$ is piecewise continuous
and large in the sense $$\liminf_{t\to \infty } \int _{t}^{t+\delta
} h>0\quad \text { for every } \delta >0. $$ The problem of intermittent
damping, initiated by P. Pucci and J. Serrin, is investigated.
Let a sequence $\{I_n=[\alpha _n, \beta _n]\}$ of disjoint intervals
be given such that $\alpha _n\to \infty $ as $n\to \infty$. A
necessary and sufficient condition is given for $I_n$ and $h$
on $I:\bigcup _{n=1}^\infty I_n$ guaranteeing $x(t)\to 0$, $x'(t)\to
0,$ as $t\to \infty $ for every solution $x,$ anyway $h$ may
be defined out of $I$''.}
\RV{J.Andres (Olomouc) |