Boundary Value Problems
Volume 2011 (2011), Article ID 172818, 19 pages
doi:10.1155/2011/172818
Research Article

Existence of Positive, Negative, and Sign-Changing Solutions to Discrete Boundary Value Problems

Bo Zheng,1 Huafeng Xiao,1 and Haiping Shi2

1School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong 510006, China
2Department of Basic Courses, Guangdong Baiyun Institute, Guangzhou, Guangdong 510450, China

Received 11 November 2010; Accepted 15 February 2011

Academic Editor: Zhitao Zhang

Copyright © 2011 Bo Zheng 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 using critical point theory, Lyapunov-Schmidt reduction method, and characterization of the Brouwer degree of critical points, sufficient conditions to guarantee the existence of five or six solutions together with their sign properties to discrete second-order two-point boundary value problem are obtained. An example is also given to demonstrate our main result.