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Locally minimising solutions of − Δu = u(1 − |u|2) in R2

Published online by Cambridge University Press:  14 November 2011

Etienne Sandier
Etienne Sandier
Affiliation:
Département de Mathématiques, Faculté des Sciences, Université Françoise Rabelais, Parc de Grandmont, 37200 Tours, France, E-mail: sandier@balzac.univ-tours.fr
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Abstract

We prove that locally minimising solutions of − Δu = u(1 − |u|2) in R2, i.e. solutions that minimise the action in any bounded domain of R2, are such that ∫R2(1 − |u|2)2(x) dx < + ∞. We prove a similar property for locally minimising solutions in a half-plane.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 2 , 1998 , pp. 349 - 358
Copyright
Copyright © Royal Society of Edinburgh 1998

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