Abstract
The topological transversality theorem is employed to study existence of solutions to a variety of singular and nonsingular second order boundary value problems of the form y″ + f( t, y, y′) = 0, 0 < t < 1. Here f may be singular at either t = 0, t = 1, y = 0, and/or y′ = 0. The principal tools are the Arzelà-Ascoli theorem, essential maps, and a priori bounds on solutions.
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