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) := -Delta[p(t - 1)Delta y(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 Green's functions for general two-point boundary value problems for Ly(t) := -Delta[p(t - 1)Delta y(t - 1)] + q(t)y(t) = 0 will also be given. (C) 2000 Elsevier Science Ltd. All rights reserved.
positive solution discrete sturm-liouville problem differentiable operators along the cone