Advances in Difference Equations
Volume 2009 (2009), Article ID 360871, 17 pages
doi:10.1155/2009/360871
Research Article

Nonlinear Discrete Periodic Boundary Value Problems at Resonance

Ruyun Ma1 and Huili Ma2

1Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2College of Economics and Management, Northwest Normal University, Lanzhou 730070, China

Received 25 June 2009; Revised 4 October 2009; Accepted 6 December 2009

Academic Editor: Kanishka Perera

Copyright © 2009 Ruyun Ma and Huili 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

Let T∈ℕ be an integer with T>2, and let 𝕋:={1,…,T}. We study the existence of solutions of nonlinear discrete problems Δ2u(t−1)+λka(t)u(t)+g(t,u(t))=h(t),  t∈𝕋,  u(0)=u(T),  u(1)=u(T+1), where a,h:𝕋→ℝ with a>0,  λk is the kth eigenvalue of the corresponding linear eigenvalue problem.