Advances in Difference Equations
Volume 2008 (2008), Article ID 345916, 10 pages
Three Solutions to Dirichlet Boundary Value Problems for -Laplacian Difference Equations
1Department of Mathematics and Computer Science, Jishou University, Jishou, Hunan 416000, China
2Department of Applied Mathematics, Hunan University, Changsha, Hunan 410082, China
3Department of Applied Mathematics, Guangzhou University, Guangzhou 510006, Guangdong, China
Received 2 March 2007; Revised 16 July 2007; Accepted 15 October 2007
Academic Editor: Svatoslav Stanek
Copyright © 2008 Liqun Jiang and Zhan Zhou. 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 deal with Dirichlet boundary value problems for -Laplacian difference equations depending on a parameter . Under some assumptions, we verify the existence of at least three solutions when lies in two exactly determined open intervals respectively. Moreover, the norms of these solutions are uniformly bounded in respect to belonging to one of the two open intervals.