Abstract and Applied Analysis
Volume 2012 (2012), Article ID 143914, 16 pages
http://dx.doi.org/10.1155/2012/143914
Research Article

Multiple Solutions for a Fractional Difference Boundary Value Problem via Variational Approach

Zuoshi Xie,1 Yuanfeng Jin,2 and Chengmin Hou2

1School of Economics and International Trade, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang 310018, China
2Department of Mathematics, Yanbian University, Yanji 133002, China

Received 28 April 2012; Revised 5 November 2012; Accepted 8 November 2012

Academic Editor: Lishan Liu

Copyright © 2012 Zuoshi Xie 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

By establishing the corresponding variational framework and using the mountain pass theorem, linking theorem, and Clark theorem in critical point theory, we give the existence of multiple solutions for a fractional difference boundary value problem with parameter. Under some suitable assumptions, we obtain some results which ensure the existence of a well precise interval of parameter for which the problem admits multiple solutions. Some examples are presented to illustrate the main results.