A generalized nonuniform contraction and Lyapunov function
type: Item
instance of: scholarly article
title: A generalized nonuniform contraction and Lyapunov function
zbMATH Open document ID: 1261.34043
DOI: 10.1155/2012/613038
author: Yongxin Jiang
author: Zhiting Xie
author: Fang-Fang Liao
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: For nonautonomous linear equations \(x' = A(t)x\), we give a complete characterization of general nonuniform contractions in terms of Lyapunov functions. We consider the general case of nonuniform contractions, which corresponds to the existence of what we call nonuniform \((D, \mu)\)-contractions. As an application, we establish the robustness of the nonuniform contraction under sufficiently small linear perturbations. Moreover, we show that the stability of a nonuniform contraction persists under sufficiently small nonlinear perturbations.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 34D10
zbMATH DE Number: 6134125
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/613038
OpenAlex ID: W2144059998
Wikidata QID: Q58695683
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description: scientific article; zbMATH DE number 6134125