Advances in Difference Equations 
Volume 2008 (2008), Article ID 469815, 11 pages
doi:10.1155/2008/469815
Research Article

On Nonresonance Problems of Second-Order Difference Systems

Ruyun Ma, Hua Luo, and Chenghua Gao

 Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
Received 8 March 2007; Revised 14 November 2007; Accepted 24 January 2008

Recommended by Alberto Cabada

Abstract

Let T be an integer with T≥3, and let T:={1,…,T}. We study the existence and uniqueness of solutions for the following two-point boundary value problems of second-order difference systems:Δ2u(t−1)+f(t,u(t))=e(t),t∈T, u(0)=u(T+1)=0, where e:T→ℝn  and  f:T×ℝn→ℝn is a potential function satisfying f(t,⋅)∈C1(ℝn) and some nonresonance conditions. The proof of the main result is based upon a mini-max theorem.