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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
Affiliation:
The University Science Institute, Dunhaga 3, 107 Reykjavik, Iceland (robmag@raunvis.hi.is)

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
Copyright
Copyright © Royal Society of Edinburgh 2006

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