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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 343129, 6 pages
http://dx.doi.org/10.1155/2014/343129
Research Article

Boundary Value Problems for Fourth Order Nonlinear -Laplacian Difference Equations

1School of Mathematics and Information Science, 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 6 October 2013; Accepted 26 December 2013; Published 30 January 2014

Academic Editor: Shih-sen Chang

Copyright © 2014 Qinqin 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

We consider the boundary value problem for a fourth order nonlinear p-Laplacian difference equation containing both advance and retardation. By using Mountain pass lemma and some established inequalities, sufficient conditions of the existence of solutions of the boundary value problem are obtained. And an illustrative example is given in the last part of the paper.