Electron. J. Diff. Equ., Vol. 2014 (2014), No. 83, pp. 1-10.

Existence and stability of solutions to nonlinear impulsive differential equations in beta-normed spaces

Jinrong Wang, Yuruo Zhang

Abstract:
In this article, we consider nonlinear impulsive differential equations in beta-normed spaces. We give new concepts of beta-Ulam's type stability. Also we present sufficient conditions for the existence of solutions for impulsive Cauchy problems. Then we obtain generalized beta-Ulam-Hyers-Rassias stability results for the impulsive problems on a compact interval. An example illustrates our main results.

Submitted February 3, 2014. Published March 26, 2014.
Math Subject Classifications: 34A37, 34D10
Key Words: Nonlinear impulsive differential equations; existence; stability.

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Jinrong Wang
Department of Mathematics, Guizhou University
Guiyang, Guizhou 550025, China
email: sci.jrwang@gzu.edu.cn
Yuruo Zhang
Department of Mathematics, Guizhou University
Guiyang, Guizhou 550025, China
email: yrzhangmath@126.com

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