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The method of the Lyapunov-Krasovskij function depending on m arguments in the problem of stability in the sense of Poisson. (Russian) Zbl 0595.34041

The second method of Lyapunov is extended to the problem of the existence of a finite number of bounded solutions of differential equations. In particular the author proves in terms of Lyapunov-Krasovskij functions sufficient conditions for the existence of compatible and uniformly compatible solutions of differential equations, i.e. solutions stable in the sense of Poisson, the recurrence character of which is of the same type as the recurrence character with respect to the time of the right- hand sides of the corresponding equations.
Reviewer: K.Barckow

MSC:

34C11 Growth and boundedness of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
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