Journal of Applied Mathematics
Volume 2012 (2012), Article ID 948345, 10 pages
http://dx.doi.org/10.1155/2012/948345
Research Article

Existence of Periodic Solutions for a Class of Asymptotically 𝑝 -Linear Discrete Systems Involving 𝑝 -Laplacian

Kai Chen1 and Qiongfen Zhang2

1Department of Information Engineering, Guilin University of Aerospace Technology, Guangxi, Guilin 541004, China
2College of Science, Guilin University of Technology, Guangxi, Guilin 541004, China

Received 20 July 2011; Accepted 16 January 2012

Academic Editor: K. S. Govinder

Copyright © 2012 Kai Chen and Qiongfen Zhang. 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

By applying Mountain Pass Theorem in critical point theory, two existence results are obtained for the following asymptotically 𝑝 -linear 𝑝 -Laplacian discrete system Δ ( | Δ 𝑢 ( 𝑡 − 1 ) | 𝑝 − 2 Δ 𝑢 ( 𝑡 − 1 ) ) + ∇ [ − 𝐾 ( 𝑡 , 𝑢 ( 𝑡 ) ) + 𝑊 ( 𝑡 , 𝑢 ( 𝑡 ) ) ] = 0 . The results obtained generalize some known works.