Absztrakt: | This paper presents an analysis of the asymptotic stability of
the system of differential equations $x' = - r(t)x + q(t)y$,
$y' = - q(t)x - p(t)y$, where $t \ge 0$ and the scalar functions
$p,q,r$ are piecewise continuous and nonnegative. A simple condition
to ensure asymptotic stability is $\int^\infty_0 \min (p(t),
r(t)) dt = + \infty$. The paper works out several other results
which use the milder assumption $\int^\infty_0 p(t)dt = + \infty$,
together with elaborate conditions of integral type. As these
conditions are somewhat technical, the author presents several
alternatives, which are less general but easier to use in applications.
Comparison with known criteria are given. The method of proof
is a combination of the method of Lyapunov functions and of the
theory of differential inequalities.}
\RV{P.Habets (Louvain-La-Neuve) |