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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.01842 |
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| _version_ | 1866914127159492608 |
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| author | Colin, Mathieu Watanabe, Tatsuya |
| author_facet | Colin, Mathieu Watanabe, Tatsuya |
| contents | This paper is devoted to the study of the nonlinear Schrödinger-Poisson system with a doping profile. We are interested in the existence of stable standing waves by considering the associated $L^2$-minimization problem. The presence of a doping profile causes a difficulty in the proof of the strict sub-additivity. A key ingredient is to establish the strict sub-additivity by adapting a scaling argument, which is inspired by \cite{ZZou}. When the doping profile is a characteristic function supported on a bounded smooth domain, smallness of some geometric quantity related to the domain ensures the existence of stable standing waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01842 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stable standing waves for Nonlinear Schrödinger-Poisson system with a doping profile Colin, Mathieu Watanabe, Tatsuya Analysis of PDEs Mathematical Physics 35J20, 35B35, 35Q55 This paper is devoted to the study of the nonlinear Schrödinger-Poisson system with a doping profile. We are interested in the existence of stable standing waves by considering the associated $L^2$-minimization problem. The presence of a doping profile causes a difficulty in the proof of the strict sub-additivity. A key ingredient is to establish the strict sub-additivity by adapting a scaling argument, which is inspired by \cite{ZZou}. When the doping profile is a characteristic function supported on a bounded smooth domain, smallness of some geometric quantity related to the domain ensures the existence of stable standing waves. |
| title | Stable standing waves for Nonlinear Schrödinger-Poisson system with a doping profile |
| topic | Analysis of PDEs Mathematical Physics 35J20, 35B35, 35Q55 |
| url | https://arxiv.org/abs/2409.01842 |