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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 879380, 6 pages
http://dx.doi.org/10.1155/2014/879380
Research Article

Multiple Solutions to Fractional Difference Boundary Value Problems

School of Mathematics and Computer Sciences, Shanxi Datong University, Datong, Shanxi 037009, China

Received 7 February 2014; Revised 6 April 2014; Accepted 6 April 2014; Published 27 April 2014

Academic Editor: Mohamed Boussairi Jleli

Copyright © 2014 Huiqin Chen 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

The following fractional difference boundary value problems , are considered, where is a real number and is the standard Riemann-Liouville fractional difference. Based on the Krasnosel’skiǐ theorem and the Schauder fixed point theorem, we establish some conditions on which are able to guarantee that this FBVP has at least two positive solutions and one solution, respectively. Our results significantly improve and generalize those in the literature. A number of examples are given to illustrate our main results.