School of Mathematical Sciences and Computing Technology, Central South University, Changsha,
Hunan 410083, China
Copyright © 2010 Peng Chen and X. H. Tang. 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 the critical point theory, we establish some existence criteria to guarantee that the nonlinear difference equation has at least one homoclinic solution, where , and is non periodic in . Our conditions on the nonlinear term are rather relaxed, and we generalize some existing results in the literature.