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: $$Delta ^{2}y(k-1)+f(k,y(k))=0,quad kin {1,ldots ,T},$$ $$y(0)=0,quad y(T+1)=alpha y(n),$$ 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.