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Singular perturbation of a nonlinear problem with multiple solutions

Published online by Cambridge University Press:  14 November 2011

Anne-Marie Lefevere
Anne-Marie Lefevere
Affiliation:
Departement de Mathématiques et d'Informatique, Faculté des Sciences, Université de Pau, 64000 Pau, France
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Synopsis

A nonlinear boundary value problem (P) having positive parameters L and a is considered. We associate with it a family of perturbed problems () affected by the presence of a barrier parameter γ related to L and a. There is a critical value L*(a) of the parameter L such that for L >L*(a), (P) has no regular solution. Then some natural extensions of (P), solutions of a free boundary value problem, arise as singular limits of ().

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 100 , Issue 3-4 , 1985 , pp. 327 - 341
Copyright
Copyright © Royal Society of Edinburgh 1985

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