Upper and lower solutions method and a superlinear singular discrete boundary value problem

Abstract

In this paper, we study the singular discrete boundary value problem {Δ[φ(Delta;u(t - 1))] + g(t,u(t)) = 0, t ∈ {1,2.....T), u(0) = u(T + 1) = 0 where φ(s) = |s|p-2s, p > 1, and the function g is superlinear at infinity and may change sign or be singular at u = 0. Existence of solutions is obtained via an upper and lower solutions method. ©Dynamic Publishers, Inc.