Existence of solutions to nonlinear Sturm-Liouville problems with large nonlinearities

Abstract

In this paper, we present results which allow us to establish the existence of solutions to nonlinear Sturm-Liouville problems with unbounded nonlinearities. We consider both regular and singular problems. Our main results rely on a variant of the Lyapunov-Schmidt used in conjunction with topological degree theory. Mathematics subject classification (2010): 34A34, 34B15, 47H11.