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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/2411.02103 |
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| _version_ | 1866917053908123648 |
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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 ground state solutions by considering the minimization problem on a Nehari-Pohozaev set. The presence of a doping profile causes several difficulties, especially in the proof of the uniqueness of a maximum point of a fibering map. A key ingredient is to establish the energy inequality. We also establish the relation between ground state solutions and $L^2$-constraint minimizers. When the doping profile is a characteristic function supported on a bounded smooth domain, some geometric quantities related to the domain, such as the mean curvature,are responsible for the existence of ground state solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02103 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ground state solutions for 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 ground state solutions by considering the minimization problem on a Nehari-Pohozaev set. The presence of a doping profile causes several difficulties, especially in the proof of the uniqueness of a maximum point of a fibering map. A key ingredient is to establish the energy inequality. We also establish the relation between ground state solutions and $L^2$-constraint minimizers. When the doping profile is a characteristic function supported on a bounded smooth domain, some geometric quantities related to the domain, such as the mean curvature,are responsible for the existence of ground state solutions. |
| title | Ground state solutions for Schrödinger-Poisson system with a doping profile |
| topic | Analysis of PDEs Mathematical Physics 35J20, 35B35, 35Q55 |
| url | https://arxiv.org/abs/2411.02103 |