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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.06988 |
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Table of Contents:
- 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.