Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 705387, 14 pages
doi:10.1155/2010/705387
Research Article

Sign-Changing Solutions for Discrete Second-Order Three-Point Boundary Value Problems

Tieshan He,1 Wei Yang,2 and Fengjian Yang1

1Department of Computation Science, Zhongkai University of Agriculture and Engineering, Guangzhou, Guangdong 510225, China
2Department of Mathematics and Physics, Fujian University of Technology, Fuzhou, Fujian 350108, China

Received 7 December 2009; Accepted 15 January 2010

Academic Editor: Leonid Shaikhet

Copyright © 2010 Tieshan He 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

We consider the second-order three-point discrete boundary value problem. By using the topological degree theory and the fixed point index theory, we provide sufficient conditions for the existence of sign-changing solutions, positive solutions, and negative solutions. As an application, an example is given to demonstrate our main results.