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2014 Linearization of Impulsive Differential Equations with Ordinary Dichotomy
Yongfei Gao, Xiaoqing Yuan, Yonghui Xia, P. J. Y. Wong
Abstr. Appl. Anal. 2014: 1-11 (2014). DOI: 10.1155/2014/632109

Abstract

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 x˙(t)=A(t)x(t)+f(t,x), ttk, Δx(tk)=A~(tk)x(tk)+f~(tk,x), k, is topologically conjugated to x˙(t)=A(t)x(t), ttk, Δx(tk)=A~(tk)x(tk), k, where Δx(tk)=x(tk+)-x(tk-), x(tk-)=x(tk), represents the jump of the solution x(t) at t=tk. Finally, two examples are given to show the feasibility of our results.

Citation

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Yongfei Gao. Xiaoqing Yuan. Yonghui Xia. P. J. Y. Wong. "Linearization of Impulsive Differential Equations with Ordinary Dichotomy." Abstr. Appl. Anal. 2014 1 - 11, 2014. https://doi.org/10.1155/2014/632109

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022783
MathSciNet: MR3178879
Digital Object Identifier: 10.1155/2014/632109

Rights: Copyright © 2014 Hindawi

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