Convergence of minimax and continuation of critical points for singularly perturbed systems

Preprint

28 October 2009

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.0910.5317

Abstract

We consider a competitive system of two stationary Gross-Pitaevskii equations arising in the theory of Bose-Einstein condensation, and the corresponding scalar equation. We address the question: "Is it true that every bounded family of solutions of the system converges, as the competition parameter goes to infinity, to a pair which difference solves the scalar equation?". We discuss this question in the case when the solutions to the system are obtained as minimax critical points via (weak) L^2 Krasnoselskii genus theory. Our results, though still partial, give a strong indication of a positive answer.

Keywords

SINGULARLY PERTURBED
COMPETITIVE SYSTEM
PERTURBED SYSTEMS
CRITICAL POINTS
SCALAR EQUATION
TWO STATIONARY
CONVERGENCE
MINIMAX

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Version 1, 2009-10-28, ArXiv

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