School of Mathematics and Computer Sciences, Shanxi Datong University, Datong, Shanxi 037008, China
Copyright © 2011 Jianmin Guo and Caixia Guo. 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.
By using Morse theory, the critical point theory, and the character
of , we consider the existence and multiplicity results of solutions to the following discrete
nonlinear two-point boundary value problem subject to , where is a positive integer, is the forward difference operator defined by , and is continuous. In argument, Morse inequalities play an important role.