Some new results for second order boundary value problems

This paper presents existence results for a variety of singular second order boundary value problems of the form y″ ± f{hook}(t, y, y′) = 0. Here, our nonlinear term f{hook} is allowed to be singular at y = 0, t = 0 and/or ft = 1. The methods used are the Topological Transversality Theorem, which is based on the notion of an essential map, and the Arzela-Ascoli Theorem.