Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 153082, 14 pages
http://dx.doi.org/10.1155/2011/153082
Research Article

Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations

Tieshan He,1 Yimin Lu,2 Youfa Lei,1 and Fengjian Yang1

1School of Computational Science, Zhongkai University of Agriculture and Engineering, Guangdong, Guangzhou 510225, China
2School of Chemistry and Chemical Engineering, Zhongkai University of Agriculture and Engineering, Guangdong, Guangzhou 510225, China

Received 4 May 2011; Accepted 29 August 2011

Academic Editor: Zengji Du

Copyright © 2011 Tieshan He et al. 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

This paper is concerned with the existence of nontrivial periodic solutions and positive periodic solutions to a nonlinear second-order difference equation. Under some conditions concerning the first positive eigenvalue of the linear equation corresponding to the nonlinear second-order equation, we establish the existence results by using the topological degree and fixed point index theories.