| Absztrakt: | The well-known Barbashin-Krasovskij theorem, which establishes
asymptotic stability for the zero solution of a differential
system by a Lyapunov function with a negative semi-definite derivative
(with respect to the given system), is extended to the partial
asymptotic stability in the sense of V. V. Rumyantsev. Contrary
to the previous extensions by {\it V. V. Rumyantsev} [Sympos.
Math. 6, 243-265 (1971; Zbl 0226.34047)], {\it A. S. Oziraner}
[Prikl. Mat. Mekh. 37, 659-665 (1973; Zbl 0295.34046)] and {\it
C. Risito} [Ann. Mat. Pura Appl., IV. Ser. 84, 279-292 (1970;
Zbl 0213.106)], the condition of the boundedness of the uncontrolled
coordinates is replaced by that not requiring "a priori" knowledge
of the solution. Moreover, some applications to the stability
properties of the equilibrium of dissipative nonholonomic mechanical
systems are given.}
\RV{M.Tvrdy |