This article is cited in 1 paper

An analog of Kamenkov's critical case for systems of ordinary differential equations with pulse action

A. I. Dvirnyĭ^a, V. I. Slyn'ko<sup>b

a</sup> Hedmark University College, Hedmark, NORWAY
^b Institute of Mechanics NAS of Ukraine, Kiev, UKRAINE

Abstract: We propose a new approach to studying the stability of systems of nonlinear differential equations with pulse action in critical cases. This approach rests on Lyapunov functions. We obtain sufficient conditions for the asymptotic stability of critical equilibria in some case analogous to Kamenkov's critical case.

Keywords: stability in the sense of Lyapunov, Kamenkov's critical case, differential equations with pulse action, Lyapunov's direct method.

UDC: 517.9

Received: 31.01.2011

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