College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
Copyright © 2010 Bo Zheng and Huafeng Xiao. 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.
This paper studies the existence of multiple solutions of the second-order difference
boundary value problem , , .
By applying Morse theory, critical groups, and the mountain pass theorem, we prove
that the previous equation
has at least three nontrivial solutions when the problem is resonant at the
eigenvalue of linear difference problem
near infinity and the trivial solution of the first equation is a local minimizer under some assumptions