A SINGULAR HARTMAN INEQUALITY FOR EXISTENCE OF SOLUTIONS TO NONLINEAR SYSTEMS OF SINGULAR, SECOND ORDER BOUNDARY VALUE PROBLEMS

Abstract

This paper examines the existence of solutions for nonlinear systems of singular, second order boundary value problems (BVPs). Topological techniques are applied to obtain new existence results for solutions to these problems. At the heart of the methods is the existence of novel {\em a priori} bounds on solutions, achieved via innovative differential inequalities. In addition, these results apply to a wide-ranging selection of singular BVPs arising in modeling of physical phenomena.