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

We consider the multi-point discrete boundary value problem with one-dimensional p-Laplacian operator Delta(phi(Delta u(t-1)) + q(t)f(t,u(t), Delta u(t) = 0, t is an element of {1,..., n-1} subject to the boundary conditions: u(0) = 0, u(n) =Sigma(m-2)(i=1) a(i)u(xi i), where phi(p)(s) = vertical bar s vertical bar(p-2) s,p > 1, xi(i) is an element of {2,..., n-2} with 1 < xi(i) < ... < xi(m-2) < n -1 and a(i) is an element of (0,1), 0 < Sigma(m-2)(i=1) ai < 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. Copyright (C) 2009 Yanping Guo et al.