Positive solutions for a second-order three-point discrete boundary value problem

We establish the existence of at least three positive solutions for the second-order three-point discrete boundary value problem: δ 2y(k-1)+f(k,y(k)=0, k∈{1,...,T}, y(0)=0, y(T+1)=αy(n) where f is continuous, T≥3 and n ∈{2,...,T-1} are two fixed positive integers, constant α>0 such that α n<T+1. Under suitable conditions, we accomplish this by using the property of the associate Green's function and Leggett-Williams fixed point theorem. © 2008 KSCAM and Springer-Verlag.