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Symmetry breaking and multiple solutions for a Neumann problem in an exterior domain

Published online by Cambridge University Press:  14 November 2011

Vittorio Coti Zelati  and
Maria J. Esteban
Vittorio Coti Zelati
Affiliation:
SISSA, Strada Costiera, 11, 34014 Trieste, Italy
Maria J. Esteban
Affiliation:
Université Pierre et Marie Curie, Laboratoire d'Analyse Numérique, 75252 Paris Cedex 05, France
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Synopsis

In this paper we prove existence of multiple positive solutions for a Neumann problem in ℝN/(0, R), R large, with a superquadratic and odd nonlinearity. The proof is based on the fact that in such a situation the minimum of the corresponding energy functional (which is achieved) is not an even function and that there is quite a large gap (for large R) between such a minimum and the minimum of the same functional on even functions. In the set of functions whose energy lies in such a gap, we can apply index theory to prove the desired multiplicity result.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 116 , Issue 3-4 , 1990 , pp. 327 - 339
Copyright
Copyright © Royal Society of Edinburgh 1990

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