Existence of positive solutions of nonlinear discrete Sturm-Liouville problems

We are concerned with proving the existence of positive solutions of two-point boundary value problems for the nonlinear discrete Sturm-Liouville equation Ly(t) := −Δ[p(t − 1)Δy(t − 1)] + q(t)y(t) = f(t,y(t)). We will use some results for differentiable operators along a certain cone in a Banach space. Useful results concerning Greenʹs functions for general two-point boundary value problems for Ly(t) := −Δ[p(t − 1)Δy(t − 1)] + q(t)y(t) = 0 will also be given.