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

Pages: 251 - 259, Volume 5, Issue 2, June 2006

doi:10.3934/cpaa.2006.5.251       Abstract        Full Text (113.9K)       Related Articles

Grey Ballard - Department of Mathematics, Wake Forest University, P.O. Box 7388, Winston-Salem, NC 27109, United States (email)
John Baxley - Department of Mathematics, Wake Forest University, P.O. Box 7388, Winston-Salem, NC 27109, United States (email)
Nisrine Libbus - Department of Mathematics, Wake Forest University, P.O. Box 7388, Winston-Salem, NC 27109, United States (email)

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.

Keywords:  Multiple solutions, qualitative behavior, shooting, iterative methods, nonlinear boundary value problems.
Mathematics Subject Classification:  Primary: 34B15, 65L10; Secondary: 65L12, 34B16, 34B18, 34A45.

Received: March 2005;      Revised: June 2005;      Published: March 2006.