On the stability in variation of non-autonomous differential equations with perturbations

M. Hammami   ; R. Hamlili   ; V. A. Zaitsev

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 2, pp. 222-247

Résumé

In this paper, we investigate the problem of stability in variation of solutions for nonautonomous differential equations. Some new sufficient conditions for the asymptotic or exponential stability for some classes of nonlinear time-varying differential equations are presented by using Lyapunov functions that are not necessarily smooth. The proposed approach for stability analysis is based on the determination of the bounds that characterize the asymptotic convergence of the solutions to a certain closed set containing the origin. Furthermore, some illustrative examples are given to prove the validity of the main results.

Détail

Keywords: nonautonomous differential equations, Lyapunov functions, asymptotic stability
Mots-clés : perturbation

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