Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 60534, 10 pages
doi:10.1155/2007/60534

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.