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arXiv · 2504.06988

Existence and order of the self--binding transition in non--local non--linear Schr\"odinger equations

Norihisa Ikoma·Krzysztof Myśliwy
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Abstract

We consider a class of non--linear and non--local functionals giving rise to the Choquard equation with a suitably regular interaction potential, modelling, i.e., gases with impurities and axion stars. We study how existence of minimizers depends on the coupling constant, and find that there is a critical interaction strength needed for the minimizers to exist, both in dimensions two and three. In $d=3$, a minimizer exists also at the critical coupling but none do in $d=2$ under suitable assumptions on the potential. We also establish that in $d=3$ there exist other critical points beyond the global minimizer.

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Norihisa Ikoma, Krzysztof Myśliwy. 2025-04-09. Existence and order of the self--binding transition in non--local non--linear Schr\"odinger equations. https://arxiv.org/abs/2504.06988

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