Qualitative behavior and computation of multiple solutions of nonlinear boundary value problems

Grey Ballard; John Baxley; Nisrine Libbus

doi:10.3934/cpaa.2006.5.251

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2006, Volume 5, Issue 2: 251-259. Doi: 10.3934/cpaa.2006.5.251

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Qualitative behavior and computation of multiple solutions of nonlinear boundary value problems

1.
Department of Mathematics, Wake Forest University, P.O. Box 7388, Winston-Salem, NC 27109

Received: February 28, 2005

Revised: May 31, 2005

Published: May 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 34B15, 65L10; Secondary: 65L12, 34B16, 34B18, 34A45.

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