On the stability in variation of non-autonomous differential equations with perturbations
type: Item
instance of: scholarly article
title: On the stability in variation of non-autonomous differential equations with perturbations
zbMATH Open document ID: 1548.34063
author: M. Hammami
author: Rabie Hamlili
author: Vasilii Zaitsev
published in: Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki
publication date: 2024-07-11T00:00:00Z
review text: In this paper, the authors investigate the problem of stability in variation of solutions for nonautonomous differential equations of the form \N\[\N\dot x=f(t,x),\tag{1}\N\]\Nwhere \(f: \mathbb{R}^+\times \mathbb{R}^n\to\mathbb{R}^n\), is a continuous function and locally Lipschitz with respect to \(x\) such that \(f(t, 0) = 0\), \(t > 0\) is time. Some new sufficient conditions for the asymptotic or exponential stability for the zero solution of system (1) 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. Some illustrative examples are given to prove the validity of the main results.
reviewed by: Alexander O. Ignatyev
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 37C60
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 7879978
zbMATH Keywords: nonautonomous differential equations
zbMATH Keywords: perturbation
zbMATH Keywords: Lyapunov functions
zbMATH Keywords: asymptotic stability
MaRDI profile type: Publication
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DOI: 10.35634/VM240204
description: scientific article; zbMATH DE number 7879978