Existence of infinite stationary solutions of the $L^2$-subcritical and critical NLSE on compact metric graphs
By Simone Dovetta. 2017
54 citations recorded by the source corpus.
We investigate the existence of stationary solutions for the Nonlinear Schr\"odinger equation on compact metric graphs. In the L2-subcritical setting, we prove the existence of an infinite number of such solutions, for every value of the mass. In the critical regime, this infinity of solutions is established to exists if and only if the mass is lower or equal to a threshold value. Moreover, the relation between this threshold and the topology of the graph is characterized. The investigation is based on variational techniques and some new versions of Gagliardo-Nirenberg inequalities.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/17f101ccd7dc141408932cb875bee9b51528d955
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In Applied Mathematics
- Nicola Soave
- Louis Jeanjean
- Xiaojun Chang
- Thomas Bartsch
- Zhi-Qiang Wang
- Wenming Zou
- Claudianor Oliveira Alves
- Vicentiu D. Rădulescu
In Mathematical Physics
- Louis Jeanjean
- Nicola Soave
- Xiaojun Chang
- Thomas Bartsch
- Xinfu Li
- Wenming Zou
- Houwang Li
- Xiaoyutao Luo
Citations in the corpus
- Normalized solutions of $L^2$-supercritical NLS equations on compact metric graphs (2022, background): “In such frameworks, a particularly relevant issue concerns the existence of ground states, that is, global minimizers of the energy under the mass constraint, see [2, 3, 4, 5] for non-compact G , and [11, 12] for the compact case.”