| Absztrakt: | The author considers the equation (1) $x'' + h(t)x' + k^2x =
0$ under the assumption (2) $0 \le h(t) \le \overline h < \infty$.
He proves that the condition $\limsup_{t \to \infty} (t^{- 2/3}
\int^t_0 h(s) ds) > 0$ is sufficient for the asymptotic stability
of $x = x' = 0$, and the exponent $2/3$ is best possible. He
obtains this as a corollary of a general result on intermittent
damping which reads as follows: Suppose that (2) is satisfied.
If there exists a sequence $\{I_n\}$ of non-overlapping intervals
such that $$\sum^\infty_{n = 1} {1 \over 1 + |I_n |^2} \left(
\int^t_0 h(s)ds \right)^3 = \infty,$$ then the zero solution
of (1) is asymptotically stable. Moreover, the exponent 3 in
the statement is best possible.}
\RV{W.M\"uller (Berlin) |