Advances in Difference Equations
Volume 2008 (2008), Article ID 469815, 11 pages
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

Academic Editor: Alberto Cabada

Copyright © 2008 Ruyun Ma et al. 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.


Let T be an integer with T3, 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(t1)+f(t,u(t))=e(t),tT, u(0)=u(T+1)=0, where e:Tn  and  f:T×nn is a potential function satisfying f(t,)C1(n) and some nonresonance conditions. The proof of the main result is based upon a mini-max theorem.