Three positive solutions for a second order difference equation with three-point boundary value problem

In this paper, we consider the solutions of discrete second-order boundary value problem {{l}Δ {2}y(k-1)+a(k)f(k,y(k))=0, k\in {1,l,T},[2pt]y(0)- αΔ y(0)=0, y(T+1)=β y(n),. where f is continuous, T3 is a fixed positive integer, n {2,T-1}, constant α,β>0 such that T+1-β n+α(1-β)>0,T+1-β n>0. Under suitable conditions, we accomplish this by using the property of the associate Green's function and Leggett-Williams fixed point theorem. © 2008 Korean Society for Computational and Applied Mathematics.