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Multiple solutions of a nonlinear boundary value problem

Published online by Cambridge University Press:  14 November 2011

William C. Troy
William C. Troy
Affiliation:
Mathematics Department, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A
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Synopsis

We consider a system of nonlinear differential equations derived from a model for the self-trapping of light. We prove that there is a parameter range for which there is a fundamental mode solution. Further, given any positive integer N, there also exists a parameter range over which the boundary value problem has N solutions. The first of these is a fundamental mode solution while the next N — 1 solutions represent additional modes.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 113 , Issue 3-4 , 1989 , pp. 191 - 209
Copyright
Copyright © Royal Society of Edinburgh 1989

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