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Solutions on a torus for a semilinear equation

Published online by Cambridge University Press:  04 April 2011

Geneviéve Allain  and
Anne Beaulieu
Geneviéve Allain
Affiliation:
Laboratoire d'Analyse et de Mathématiques Appliquées, UMR CNRS 8050, Faculté de Sciences et Technologie, Université Paris-Est Créteil Val de Marne, 61 avenue du Général de Gaulle, 94010 Créteil cedex, Franceallain@u-pec.fr
Anne Beaulieu
Affiliation:
Laboratoire d'Analyse et de Mathématiques Appliquées, UMR CNRS 8050, Université Paris-Est Marne la Vallée, 5 boulevard Descartes, 77454 Marne la Vallée cedex 2, Franceanne.beaulieu@univ-paris-est.fr
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Abstract

We are interested in the positive doubly periodic solutions, which are even in each variable, of a stationary nonlinear Schrödinger equation in ℝ2, with a small parameter. For any pair of periods (2a, 2b), we construct a branch of solutions that concentrate uniformly to the ground-state solution of the equation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 2 , April 2011 , pp. 371 - 382
Copyright
Copyright © Royal Society of Edinburgh 2011

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