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Bounded solutions for an ordinary differential system from the Ginzburg–Landau theory

Part of: Boundary value problems Spectral theory and eigenvalue problems Elliptic equations and systems

Published online by Cambridge University Press:  14 August 2020

Anne Beaulieu
Anne Beaulieu*
Affiliation:
LAMA, Univ. Paris Est Creteil, Univ. Gustave Eiffel, UPEM, CNRS, F-94010, Créteil, France (anne.beaulieu@u-pec.fr)
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Abstract

In this paper, we look at a linear system of ordinary differential equations as derived from the two-dimensional Ginzburg–Landau equation. In two cases, it is known that this system admits bounded solutions coming from the invariance of the Ginzburg–Landau equation by translations and rotations. The specific contribution of our work is to prove that in the other cases, the system does not admit any bounded solutions. We show that this bounded solution problem is related to an eigenvalue problem.

Keywords

Ginzburg–Landau equationslinearized operator

MSC classification

Primary: 34B40: Boundary value problems on infinite intervals
Secondary: 35J60: Nonlinear elliptic equations 35P15: Estimation of eigenvalues, upper and lower bounds
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 6 , December 2020 , pp. 3378 - 3408
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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