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Matematicheskie Zametki, 2013, Volume 93, Issue 5, Pages 702–715
DOI: https://doi.org/10.4213/mzm9136 (Mi mzm9136) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Stability of Solutions of Pseudolinear Differential Equations with Impulse Action

A. I. Dvirnyja, V. I. Slyn'kob

a Academy of Fire Secyrity
b Institute of Mechanics named after S. P. Timoshenko of National Academy of Sciences of Ukraine
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DOI: https://doi.org/10.4213/mzm9136
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.
Received: 21.04.2011
Revised: 30.06.2012
English version:
Mathematical Notes, 2013, Volume 93, Issue 5, Pages 691–703
DOI: https://doi.org/10.1134/S0001434613050052
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. I. Dvirnyj, V. I. Slyn'ko, “Stability of Solutions of Pseudolinear Differential Equations with Impulse Action”, Mat. Zametki, 93:5 (2013), 702–715; Math. Notes, 93:5 (2013), 691–703
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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