| Absztrakt: | Conditions are given guaranteeing the property $x(t) \to 0$,
$\dot x(t) \to 0$ $(t \to \infty)$ for every solution of the
equation $\ddot x+h(t) \dot x+k\sp 2x=0$ $(t \ge 0, 0<k=\text{const.})$,
where $h$ is a nonnegative function. It is known that this property
requires that in the average the damping coefficient $h$ is not
``too small'' or ``too large''. In the first part we give a necessary
and sufficient growth condition on $h$, provided that $h$ is
not ``too small'' in some integral sense. Then, considering the
case of small $h$, we show that not only the size, but the distribution
of the damping ``bumps'' is important. The main theorem takes
into account both of them. Finally, we formulate theorems for
the general case when $h$ can be both small and large. It is
pointed out that the conditions restricting $h$ above and below
are interdependent. |