Existence of Positive Solutions of a Sturm-Liouville Bvp on an Unbounded Time Scale

Abstract

A fixed point theorem of Guo-Krasnoselskii type is used to establish existence results for the nonlinear Sturm-Liouville dynamic equation (p(t)x(Delta))(del) + lambda phi(t)f(t,x(t)) = 0 with the boundary conditions on an unbounded time scale. Later on the positivity and the boundedness of the solutions are obtained by imposing some conditions on f.