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
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.
Abstract
Consider the multiplicity of solutions to the nonlinear second-order discrete problems with
minimum and maximum: Δ2u(k−1)=f(k,u(k),Δu(k)), k∈T,
min{u(k):k∈T^}=A,
max{u(k):k∈T^}=B,
where f:T×ℝ2→ℝ, a,b∈ℕ are fixed numbers satisfying b≥a+2, and A,B∈ℝ are satisfying
B>A,
T={a+1,…,b−1}, T^={a,a+1,…,b−1,b}.