Advances in Difference Equations
Volume 2007 (2007), Article ID 96415, 12 pages
doi:10.1155/2007/96415

Unbounded perturbations of nonlinear second-order difference equations at resonance

Abstract

We study the existence of solutions of nonlinear discrete boundary value problems Δ2u(t−1)+μ1u(t)+g(t,u(t))=h(t), t∈T, u(a)=u(b+2)=0, where T:={a+1,…, b+1}, h:T→ℝ, μ1 is the first eigenvalue of the linear problem Δ2u(t−1)+μu(t)=0, t∈T, u(a)=u(b+2)=0, g:T×ℝ→ℝ satisfies some “asymptotic nonuniform” resonance conditions, and g(t,u)u≥0 for u∈ℝ.