Qualitative Behavior and Computation of Multiple Solutions of Singular Nonlinear Boundary Value Problems

The present work is a first attempt to understand singular boundary value problems with multiple solutions. As such, it seeks to combine research on singular boundary value problems having unique solutions that began with the paper of Taliaferro [9] with work on nonsingular boundary value problems having multiple solutions that received impetus from the paper by Henderson and Thompson [7] but dates back at least to work by Parter [8]. The majority of later papers dealt with theoretical questions of existence, but a few, such as [1, 3, 5], have dealt with computational questions. We shall focus here on two examples, which have the form