On Sturm - Liouville and Thomas - Fermi Singular Boundary-Value Problems

Abstract

In this paper we investigate the existence of a positive solution of a second order singular Sturm – Liouville boundary-value problem, by constructing upper and lower solutions and combined them with properties of the consequent mapping. Applications to well known Emden – Fowler and Thomas – Fermi boundary-value problems are also presented. Further we generalize some of O’Regan’s results, allowing constants in the boundary conditions to be negative.