Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Three Solutions to Dirichlet Boundary Value Problems for p-Laplacian Difference Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2008 Article ID 345916 10 pages doi 2008 345916 Research Article Three Solutions to Dirichlet Boundary Value Problems for p-Laplacian Difference Equations Liqun Jiang1 2 and Zhan Zhou2 3 1 Department of Mathematics and Computer Science Jishou University Jishou Hunan 416000 China 2 Department of Applied Mathematics Hunan University Changsha Hunan 410082 China 3 Department of Applied Mathematics Guangzhou University Guangzhou 510006 Guangdong China Correspondence should be addressed to Liqun Jiang liqunjianghn@ Received 2 March 2007 Revised 16 July 2007 Accepted 15 October 2007 Recommended by Svatoslav Stanek We deal with Dirichlet boundary value problems for p-Laplacian difference equations depending on a parameter 1. Under some assumptions we verify the existence of at least three solutions when 1 lies in two exactly determined open intervals respectively. Moreover the norms of these solutions are uniformly bounded in respect to 1 belonging to one of the two open intervals. Copyright 2008 L. Jiang and Z. 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. 1. Introduction Let R Z N be all real numbers integers and positive integers respectively. Denote Z a a a 1 . and Z a b a a 1 . b with a b for any a b G Z. In this paper we consider the following discrete Dirichlet boundary value problems A ệp Ax k -1 If fk x k 0 k G Z 1 T x 0 0 x J 1 where T is a positive integer p 1 is a constant A is the forward difference operator defined by Ax k x k 1 - x k ệp s is a p-Laplacian operator that is ệp s s p-2s f k G C R R for any k G Z 1 T . There seems to be increasing interest in the existence of solutions to boundary value problems for finite difference equations with p-Laplacian operator because of their applications in many .
