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June  2006, 5(2): 251-259. doi: 10.3934/cpaa.2006.5.251

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

Grey Ballard 1, , John Baxley 1, and  Nisrine Libbus 1,

1. 

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

Received  March 2005 Revised  June 2005 Published  March 2006

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.
Keywords: shooting, Multiple solutions, nonlinear boundary value problems., iterative methods, qualitative behavior.
Mathematics Subject Classification: Primary: 34B15, 65L10; Secondary: 65L12, 34B16, 34B18, 34A4.
Citation: Grey Ballard, John Baxley, Nisrine Libbus. Qualitative behavior and computation of multiple solutions of nonlinear boundary value problems. Communications on Pure & Applied Analysis, 2006, 5 (2) : 251-259. doi: 10.3934/cpaa.2006.5.251
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