Advances in Difference Equations
Volume 2008 (2008), Article ID 586020, 16 pages
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

Academic Editor: Svatoslav Staněk

Copyright © 2008 Ruyun Ma and Chenghua Gao. 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.


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}.