Positive and Monotone Solutions of a Complete Sturm-Liouville Boundary Value Problem

Abstract

Consider a full second order nonlinear scalar differential equations where the nonlinearities is negative, associated to some linear Sturm-Liouville boundary conditions with their coefficients not always positive. Existence results of positive (and monotonous at some cases) solutions of above BVPs are given, under superlinear and/or sublinear growth in f. The approach is based on an analysis of the corresponding vector field on the face-plane and Kneser's property of solutions funnel.