The planar Schrodinger--Poisson system with exponential critical growth: The local well-posedness and standing waves with prescribed mass
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909620107214848 |
|---|---|
| author | Sun, Juntao Yao, Shuai Zhang, Jian |
| author_facet | Sun, Juntao Yao, Shuai Zhang, Jian |
| contents | In this paper, we investigate a class of planar Schrödinger-Poisson systems with critical exponential growth. We establish conditions for the local well-posedness of the Cauchy problem in the energy space, which seems innovative as it was not discussed at all in any previous results. By introducing some new ideas and relaxing some of the classical growth assumptions on the nonlinearity, we show that such system has at least two standing waves with prescribed mass, where one is a ground state standing waves with positive energy, and the other one is a high-energy standing waves with positive energy. In addition, with the help of the local well-posedness, we show that the set of ground state standing waves is orbitally stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00159 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The planar Schrodinger--Poisson system with exponential critical growth: The local well-posedness and standing waves with prescribed mass Sun, Juntao Yao, Shuai Zhang, Jian Analysis of PDEs In this paper, we investigate a class of planar Schrödinger-Poisson systems with critical exponential growth. We establish conditions for the local well-posedness of the Cauchy problem in the energy space, which seems innovative as it was not discussed at all in any previous results. By introducing some new ideas and relaxing some of the classical growth assumptions on the nonlinearity, we show that such system has at least two standing waves with prescribed mass, where one is a ground state standing waves with positive energy, and the other one is a high-energy standing waves with positive energy. In addition, with the help of the local well-posedness, we show that the set of ground state standing waves is orbitally stable. |
| title | The planar Schrodinger--Poisson system with exponential critical growth: The local well-posedness and standing waves with prescribed mass |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2305.00159 |