Existence theory for single and multiple solutions to singular positone discrete dirichlet boundary value problems to the one-dimension p-Laplacian

In this paper we establish the existence of single and multiple solutions to the positone discrete Dirichlet boundary value problem { Δ[φ(Δu(t-1))] + q(t) f(t, u(t)) = 0, t ∈ {1, 2,...,T} u(0) = u(T + 1) = 0, where φ(s) = |s|^p-2s, p > 1 and our nonlinear term f(t, u) may be singular at u = 0.