Eigenvalues and discrete boundary value problems for the one-dimensional p-laplacian

In this paper, we characterize the eigenvalues and show existence of positive solutions to discrete boundary value problem (here φ(s) = |s|p−2s, p >1 and λ>0 is a parameter) Δ(φ(Δu(i −1)))+ λF(i, u(i)) = 0, i ∈ N = {1, 2, . . . , T }; u(0) = u(T + 1) = 0.  2004 Elsevier Inc. All rights reserved.