Abstract and Applied Analysis

Linearization of Impulsive Differential Equations with Ordinary Dichotomy

Yongfei Gao, Xiaoqing Yuan, Yonghui Xia, and P. J. Y. Wong

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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 ) , t t k , Δ x ( t k ) = A ~ ( t k ) x ( t k ) + f ~ ( t k , x ) , k , is topologically conjugated to x ˙ ( t ) = A ( t ) x ( t ) , t t k , Δ x ( t k ) = A ~ ( t k ) x ( t k ) , k , where Δ 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.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 632109, 11 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273208

Digital Object Identifier
doi:10.1155/2014/632109

Mathematical Reviews number (MathSciNet)
MR3178879

Zentralblatt MATH identifier
07022783

Citation

Gao, Yongfei; Yuan, Xiaoqing; Xia, Yonghui; Wong, P. J. Y. Linearization of Impulsive Differential Equations with Ordinary Dichotomy. Abstr. Appl. Anal. 2014 (2014), Article ID 632109, 11 pages. doi:10.1155/2014/632109. https://projecteuclid.org/euclid.aaa/1412273208


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