Positive solutions of singular boundary value problems.

Abstract

In this dissertation, we focus on singular boundary value problems with mixed boundary conditions. We study a variety of types, to all of which we seek a positive solution. We begin by considering the discrete (or difference equation) case, from which we proceed to look at the continuous (or ordinary differential equation) case. In all cases, we make use of a lower and upper solutions method and the Brouwer fixed point theorem in conjunction with perturbation methods to approximate regular problems.