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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 for a Discrete Nonlinear Neumann Problem Involving the p-Laplacian Pasquale Candito1 and Giuseppina D’Agu`2 ı | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 862016 11 pages doi 10.1155 2010 862016 Research Article Three Solutions for a Discrete Nonlinear Neumann Problem Involving the p-Laplacian Pasquale Candito1 and Giuseppina D Agui2 1 DIMET University of Reggio Calabria Via Graziella Feo Di Vito 89100 Reggio Calabria Italy 2 Department of Mathematics of Messina DIMET University of Reggio Calabria 89100 Reggio Calabria Italy Correspondence should be addressed to Giuseppina D Agul dagui@unime.it Received 26 October 2010 Accepted 20 December 2010 Academic Editor E. Thandapani Copyright 2010 P. Candito and G. D Agul. 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 investigate the existence of at least three solutions for a discrete nonlinear Neumann boundary value problem involving the p-Laplacian. Our approach is based on three critical points theorems. 1. Introduction In these last years the study of discrete problems subject to various boundary value conditions has been widely approached by using different abstract methods as fixed point theorems lower and upper solutions and Brower degree see e.g. 1-3 and the reference given therein . Recently also the critical point theory has aroused the attention of many authors in the study of these problems 4-12 . The main aim of this paper is to investigate different sets of assumptions which guarantee the existence and multiplicity of solutions for the following nonlinear Neumann boundary value problem -A ệp àuk-ỉ qkệptuk Xf k Uk k e 1 N Au0 AuN 0 Pff where N is a fixed positive integer 1 N is the discrete interval 1 . N qk 0 for all k e 1 N X is a positive real parameter Auk uk i - uk k 0 1 . N 1 is the forward difference operator ộp s s p-2s 1 p TO and f 1 N xR R is a continuous function. 2 Advances in Difference Equations In
