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

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

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.