UPPER AND LOWER SOLUTIONS METHOD AND A SUPERLINEAR SINGULAR DISCRETE BOUNDARY VALUE PROBLEM

In this paper, we study the singular discrete boundary value problem    ∆[φ(∆u(t − 1))] + g(t, u(t)) = 0, t ∈ {1, 2, . . . , T}, u(0) = u(T + 1) = 0 where φ(s) = |s| p−2 s, 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.