NLS ground states on metric trees: existence results and open questions

@article{Dovetta2019NLSGS,
  title={NLS ground states on metric trees: existence results and open questions},
  author={Simone Dovetta and Enrico Serra and Paolo Tilli},
  journal={arXiv: Analysis of PDEs},
  year={2019}
}
We consider the minimization of the NLS energy on a metric tree, either rooted or unrooted, subject to a mass constraint. With respect to the same problem on other types of metric graphs, several new features appear, such as the existence of minimizers with positive energy, and the emergence of unexpected threshold phenomena. We also study the problem with a radial symmetry constraint that is in principle different from the free problem due to the failure of the Polya-Szegő inequality for… Expand

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