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Abstract and Applied Analysis
Volume 2016, Article ID 5098086, 7 pages
http://dx.doi.org/10.1155/2016/5098086
Research Article

New Conditions for the Exponential Stability of Pseudolinear Difference Equations in Banach Spaces

Departamento de Ciencias Exactas, Universidad de Los Lagos, Casilla 933, 5290000 Osorno, Chile

Received 28 December 2015; Revised 18 March 2016; Accepted 24 March 2016

Academic Editor: Patricia J. Y. Wong

Copyright © 2016 Rigoberto Medina. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the local exponential stability of evolution difference systems with slowly varying coefficients and nonlinear perturbations. We establish the robustness of the exponential stability in infinite-dimensional Banach spaces, in the sense that the exponential stability for a given pseudolinear equation persists under sufficiently small perturbations. The main methodology is based on a combined use of new norm estimates for operator-valued functions with the “freezing” method.