Advances in Difference Equations
Volume 2007 (2007), Article ID 96415, 12 pages
doi:10.1155/2007/96415
Research Article
Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
Received 19 March 2007; Accepted 30 May 2007
Academic Editor: Johnny L. Henderson
Copyright © 2007 Ruyun Ma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.