| Absztrakt: | The author continues his earlier study of partial stability of
the zero solution of $x'=X(x)$ using Lyapunov's direct method
[ibid. 46, 143-156 (1983; Zbl 0524.34057)]. The vector x is decomposed
as $x=(y,z)$ and the equation is then written as (E) $y'=Y(y,z)$,
$z'=Z(y,z)$. In this paper the author treats the case where the
right-hand side Y has a uniform limit as the vector z of uncontrolled
coordinates tends to infinity in norm. Conditions for the zero
solution of (E) to be asymptotically y- stable are given. Extensions
to the nonautonomous system (F) $y'=Y(y,z,t)$, $z'=Z(y,z,t)$
are also given.}
\RV{P.K.Wong |