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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 567471, 10 pages
http://dx.doi.org/10.1155/2014/567471
Research Article

Nonconstant Periodic Solutions of Discrete -Laplacian System via Clark Duality and Computations of the Critical Groups

1College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong 510006, China
2Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong 510006, China

Received 18 October 2013; Accepted 2 January 2014; Published 12 February 2014

Academic Editor: Svatoslav Staněk

Copyright © 2014 Bo Zheng. 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 existence of periodic solutions to a discrete -Laplacian system. By using the Clark duality method and computing the critical groups, we find a simple condition that is sufficient to ensure the existence of nonconstant periodic solutions to the system.