Existence and Multiplicity of Normalized Solutions to Schrödinger Equations with General Nonlinearities in Bounded Domains
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911010156183552 |
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| author | Ji, Wei |
| author_facet | Ji, Wei |
| contents | This paper focuses on the existence of multiple normalized solutions to Schrödinger equations with general nonlinearities in bounded domains via variational methods. We first obtain two positive normalized solutions, one is a normalized ground state by searching for a local minimizer, and the other one is a mountain pass solution. Secondly, using a version of Linking theorems for normalized solutions, we prove the multiplicity of solutions to Schrödinger equations in a star-shaped bounded domain. Moreover, we arrive at the existence of nonradial normalized solutions to Schrödinger equations in a ball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15089 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and Multiplicity of Normalized Solutions to Schrödinger Equations with General Nonlinearities in Bounded Domains Ji, Wei Analysis of PDEs 35A01 35B09, 35A15, 35B40, 35J60 This paper focuses on the existence of multiple normalized solutions to Schrödinger equations with general nonlinearities in bounded domains via variational methods. We first obtain two positive normalized solutions, one is a normalized ground state by searching for a local minimizer, and the other one is a mountain pass solution. Secondly, using a version of Linking theorems for normalized solutions, we prove the multiplicity of solutions to Schrödinger equations in a star-shaped bounded domain. Moreover, we arrive at the existence of nonradial normalized solutions to Schrödinger equations in a ball. |
| title | Existence and Multiplicity of Normalized Solutions to Schrödinger Equations with General Nonlinearities in Bounded Domains |
| topic | Analysis of PDEs 35A01 35B09, 35A15, 35B40, 35J60 |
| url | https://arxiv.org/abs/2409.15089 |