A New Method to prove the Existence, Non-existence, Multiplicity, Uniqueness, and Orbital Stability/Instability of standing waves for NLS with partial confinement
| Autor: | Song, Linjie, Hajaiej, Hichem |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We give a new method to prove the existence, non-existence, multiplicity, orbital stability/instability of standing waves for NLS with partial confinement without the subcritical hypothesis, even in the reduction equation. Using this method, we give an affirmative answer for an open problem proposed by [7, Remark 1.10] where the authors conjectured the existence of more than a normalized solution. We also establish uniqueness results of the ground state solutions depending on the bifurcation parameters. We explain that when the effect of partial confinement is strong, a dimension reduction appears for some parameters. We also find different bifurcation phenomena from the cases with full confinement. Comment: The authors welcome any comments. Please don't hesitate to share them with both authors at songlinjie18@mails.ucas.edu.cn and hichem.hajaiej@gmail.com. Thank you! |
| Databáze: | arXiv |
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