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Qualitative behavior and computation of multiple solutions of nonlinear boundary value problems
We consider nonlinear boundary value problems with multiple
solutions. A method is proposed for the computation of such
solutions which depends crucially on known
a priori
qualitative
information about the behavior of the solutions. The method is
a two-stage method where the second stage is a shooting method
and initial values of the shooting parameters are found in a first
stage which approximates the boundary value problem with a discrete
approximation. Both nonsingular and singular problems are considered.