Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 714179, 10 pages
doi:10.1155/2009/714179
Research Article

Infinitely Many Periodic Solutions for Variable Exponent Systems

Xiaoli Guo,1 Mingxin Lu,2 and Qihu Zhang1

1Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, China
2Department of Information Management, Nanjing University, Nanjing 210093, China

Received 4 December 2008; Accepted 14 April 2009

Academic Editor: Marta Garcia-Huidobro

Copyright © 2009 Xiaoli Guo 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

We mainly consider the system −Δp(x)u=f(v)+h(u) in ℝ, −Δq(x)v=g(u)+ω(v) in ℝ, where 1<p(x),q(x)∈C1(ℝ) are periodic functions, and −Δp(x)u=−(|u′|p(x)−2u′)′ is called p(x)-Laplacian. We give the existence of infinitely many periodic solutions under some conditions.