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

Existence and multiple solutions for nonlinear second-order discrete problems with minimum and maximum

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}.