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The implicit function theorem and multi-bump solutions of periodic partial differential equations

Published online by Cambridge University Press:  30 July 2007

Robert Magnus
Robert Magnus
Affiliation:
The University Science Institute, Dunhaga 3, 107 Reykjavik, Iceland ([email protected])
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Abstract

A modification of the implicit function theorem is advanced for cases where the continuity of the derivative fails. It is applied to a superposition principle for periodicpartial differential equations. The assumption of the principle, that there should exist a non-degenerate solution, is studied and instances of it realized using perturbation arguments and scaling. The positivity of solutions is considered.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 3 , June 2006 , pp. 559 - 583
Copyright
Copyright © Royal Society of Edinburgh 2006

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