Advances in Difference Equations
Volume 2006 (2006), Article ID 82784, 9 pages
doi:10.1155/ADE/2006/82784

Positive solutions of functional difference equations with p-Laplacian operator

Chang-Xiu Song1,2

1School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
2School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China

Received 18 October 2005; Accepted 10 January 2006

Copyright © 2006 Chang-Xiu Song. 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.

Abstract

The author studies the boundary value problems with p-Laplacian functional difference equation Δφp(Δx(t))+r(t)f(xt)=0, t∈[0,N], x0=ψ∈C+, x(0)−B0(Δx(0))=0, Δx(N+1)=0. By using a fixed point theorem in cones, sufficient conditions are established for the existence of twin positive solutions.