Advances in Difference Equations 
Volume 2008 (2008), Article ID 586020, 16 pages
doi:10.1155/2008/586020
Research Article

Existence and Multiple Solutions for Nonlinear Second-Order Discrete Problems with Minimum and Maximum

Ruyun Ma and Chenghua Gao

College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, China

Received 15 March 2008; Revised 6 June 2008; Accepted 19 July 2008

Recommended by Svatoslav Staněk

Abstract

Consider the multiplicity of solutions to the nonlinear second-order discrete problems with minimum and maximum: Δ2u(k1)=f(k,u(k),Δu(k)), kT, min{u(k):kT^}=A, max{u(k):kT^}=B, where f:T×2,a,b are fixed numbers satisfying ba+2,andA,B are satisfying B>A, T={a+1,,b1},T^={a,a+1,,b1,b}.