Existence of Positive, Negative, and Sign-Changing Solutions to Discrete Boundary Value Problems
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
Boundary Value Problems 2011, 2011:172818 doi:10.1155/2011/172818Published: 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.