Advances in Difference Equations
Volume 2006 (2006), Article ID 89585, 7 pages
doi:10.1155/ADE/2006/89585

Multiple nonnegative solutions for BVPs of fourth-order difference equations

Abstract

First, existence criteria for at least three nonnegative solutions to the following boundary value problem of fourth-order difference equation Δ4x(t−2)=a(t)f(x(t)), t∈[2,T], x(0)=x(T+2)=0, Δ2x(0)=Δ2x(T)=0 are established by using the well-known Leggett-Williams fixed point theorem, and then, for arbitrary positive integer m, existence results for at least 2m-1 nonnegative solutions are obtained.