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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 949487, 8 pages
http://dx.doi.org/10.1155/2014/949487
Research Article

Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations

Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, Zhejiang 310023, China

Received 17 March 2014; Accepted 21 July 2014; Published 10 August 2014

Academic Editor: Zhan Zhou

Copyright © 2014 Zhinan Xia. 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 define the concept of discrete weighted pseudo--asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo--asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem.