Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 538431, 15 pages
Research Article

Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-Laplacian

College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China

Received 23 May 2009; Accepted 18 October 2009

Academic Editor: Leonid Shaikhet

Copyright © 2009 Yanping Guo et al. 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 consider the multi-point discrete boundary value problem with one-dimensional p-Laplacian operator Δ(ϕp(Δu(t1))+q(t)f(t,u(t),Δu(t))=0, t{1,,n1} subject to the boundary conditions: u(0)=0, u(n)=i=1m2aiu(ξi), where ϕp(s)=|s|p2s,p>1,ξi{2,,n2} with 1<ξ1<<ξm2<n1 and ai(0,1),0<i=1m2ai<1. Using a new fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.