Linearization of impulsive differential equations with ordinary dichotomy
type: Item
instance of: scholarly article
title: Linearization of impulsive differential equations with ordinary dichotomy
zbMATH Open document ID: 1474.34259
DOI: 10.1155/2014/632109
author: Yongfei Gao
author: Xiaoqing Yuan
author: Yonghui Xia
author: Patricia J. Y. Wong
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: This paper presents a linearization theorem for the impulsive differential equations when the linear system has ordinary dichotomy. We prove that when the linear impulsive system has ordinary dichotomy, the nonlinear system \(\dot{x}(t) = A(t) x(t) + f(t, x)\), \(t \neq t_k\), \(\Delta x(t_k) = \widetilde{A}(t_k) x(t_k) + \widetilde{f}(t_k, x)\), \(k \in \mathbb Z\), is topologically conjugated to \(\dot{x}(t) = A(t) x(t)\), \(t \neq t_k\), \(\Delta x(t_k) = \widetilde{A}(t_k) x(t_k)\), \(k \in \mathbb Z\), where \(\Delta x(t_k) = x(t_k^+) - x(t_k^-)\), \(x(t_k^-) = x(t_k)\), represents the jump of the solution \(x(t)\) at \(t = t_k\). Finally, two examples are given to show the feasibility of our results.
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 34D09
zbMATH DE Number: 7022783
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/632109
OpenAlex ID: W2159304711
Wikidata QID: Q59040213
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description: scientific article; zbMATH DE number 7022783