Advances in Difference Equations
Volume 2010 (2010), Article ID 195376, 17 pages
Research Article

On Homoclinic Solutions of a Semilinear 𝑝 -Laplacian Difference Equation with Periodic Coefficients

1Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
2Department of Mathematics, Minzu University of China, Beijing 100081, China
3Department of Mathematical Analysis, University of Rousse, 7017 Rousse, Bulgaria

Received 5 July 2010; Accepted 27 October 2010

Academic Editor: Jianshe Yu

Copyright © 2010 Alberto Cabada et al. 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.


We study the existence of homoclinic solutions for semilinear 𝑝 -Laplacian difference equations with periodic coefficients. The proof of the main result is based on Brezis-Nirenberg's Mountain Pass Theorem. Several examples and remarks are given.