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

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.