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

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

2009-10-28

arxiv.org/abs/0910.5317v1

Mathematics

Analysis of PDEs

25 pages

Scientific paper

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.

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