Existence of Triple Positive Solutions for Second-Order Discrete Boundary Value Problems

Abstract

By using a new fixed-point theorem introduced by Avery and Peterson (2001), we obtain sufficient conditions for the existence of at least three positive solutions for the equation Δ2x(k−1)+q(k)f(k,x(k),Δx(k))=0, for k∈{1,2,…,n−1}, subject to the following two boundary conditions: x(0)=x(n)=0 or x(0)=Δx(n−1)=0, where n≥3.