This article is cited in 1 paper

Stability of Solutions of Pseudolinear Differential Equations with Impulse Action

A. I. Dvirnyj^a, V. I. Slyn'ko<sup>b

a</sup> Academy of Fire Secyrity
^b Institute of Mechanics named after S. P. Timoshenko of National Academy of Sciences of Ukraine

Abstract: In this paper, we develop a new approach to constructing piecewise differentiable Lyapunov functions for certain classes of nonlinear differential equations with impulse action. This approach is based on the method of “frozen” coefficients, and the required function is constructed as a pseudoquadratic form. For the case under consideration, stability conditions in the sense of Lyapunov are obtained. The proposed approach can be used to study the stability of the critical equilibrium states of systems of differential equations with impulse action.

Keywords: pseudodifferential equation with impulse action, Lyapunov stability of solutions of differential equations, pseudoquadratic form, critical equilibrium state, method of “frozen” coefficients.

UDC: 517.9

Received: 21.04.2011
Revised: 30.06.2012

DOI: 10.4213/mzm9136

 English version: Mathematical Notes, 2013, 93:5, 691–703

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