Normalized solutions for the planar Schrödinger-Poisson system with two electrons interaction
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911296387022848 |
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| author | Li, Baihong Wei, Yuanhong Zeng, Xiangjian |
| author_facet | Li, Baihong Wei, Yuanhong Zeng, Xiangjian |
| contents | This paper focuses on the normalized solutions for the planar Schrödinger-Poisson system with a two-electron interaction, which models the effect between electrons and the electrostatic potential they generate. As the parameters vary, some existence results are established. Specifically, a ground state solution is obtained for some general cases. The existence of two solutions is established for the mass-supercritical case, one of which is a ground state solution and the other one is an excited state solution. We develop a compactness method to deal with the functionals involving logarithmic convolution terms. The Pohožaev identity for the coupled Schrödinger-Poisson system with a logarithmic convolution term is also shown, which is crucial for addressing the mass-supercritical problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01655 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normalized solutions for the planar Schrödinger-Poisson system with two electrons interaction Li, Baihong Wei, Yuanhong Zeng, Xiangjian Analysis of PDEs This paper focuses on the normalized solutions for the planar Schrödinger-Poisson system with a two-electron interaction, which models the effect between electrons and the electrostatic potential they generate. As the parameters vary, some existence results are established. Specifically, a ground state solution is obtained for some general cases. The existence of two solutions is established for the mass-supercritical case, one of which is a ground state solution and the other one is an excited state solution. We develop a compactness method to deal with the functionals involving logarithmic convolution terms. The Pohožaev identity for the coupled Schrödinger-Poisson system with a logarithmic convolution term is also shown, which is crucial for addressing the mass-supercritical problem. |
| title | Normalized solutions for the planar Schrödinger-Poisson system with two electrons interaction |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.01655 |