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

Benedetta NorisHugo TavaresSusanna TerraciniGianmaria Verzini — 2012

Journal of the European Mathematical Society

In the recent literature, the phenomenon of phase separation for binary mixtures of Bose–Einstein condensates can be understood, from a mathematical point of view, as governed by the asymptotic limit of the stationary Gross–Pitaevskii system - Δ u + u 3 + β u v 2 = λ u , - Δ v + v 3 + β u 2 v = μ v , u , v H 0 1 ( Ω ) , u , v > 0 , as the interspecies scattering length β goes to + . For this system we consider the associated energy functionals J β , β ( 0 , + ) , with L 2 -mass constraints, which limit J (as β + ) is strongly irregular. For such functionals, we construct multiple critical points via a common...

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