SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research Article

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

Bo Zheng1*, Huafeng Xiao1 and Haiping Shi2

Author Affiliations

1 School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong 510006, China

2 Department of Basic Courses, Guangdong Baiyun Institute, Guangzhou, Guangdong 510450, China

For all author emails, please log on.

Boundary Value Problems 2011, 2011:172818  doi:10.1155/2011/172818

Published: 10 March 2011


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.