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On partial stability of a dynamic system that is integrally continuous with respect to a small parameter. (English. Russian original) Zbl 0869.34043

J. Math. Sci., New York 82, No. 3, 3420-3424 (1996); translation from Din. Sist. (Kiev) 13, 29-36 (1994).
Summary: For a dynamic system described by Carathéodory ordinary differential equations with a small parameter we introduce the definitions of a type of partial stability, attraction, and asymptotic stability. We state theorems giving sufficient conditions for stability in the new definitions. In particular, in terms of perturbed Lyapunov functions we obtain conditions for partial asymptotic stability that generalize known results.

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
34D10 Perturbations of ordinary differential equations
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References:

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