Normalized solutions on large smooth domains to the Schrödinger equations with potential and combined nonlinearities: The Sobolev critical case
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915088902914048 |
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| author | Lin, Xiaolu Liu, Yanjun Lv, Zongyan |
| author_facet | Lin, Xiaolu Liu, Yanjun Lv, Zongyan |
| contents | In this paper, we consider the existence and multiplicity of prescribed mass solutions to the following nonlinear Schrodinger equations with mixed nonlinearities. The standard approach based on the Pohozaev identity to obtain normalized solutions is invalid as the presence of potential. Besides, Our study can be regarded as a Sobolev critical case complement of Bartsch-Qi-Zou (Math Ann 390, 4813-4859, 2024), which has addressed an open problem raised in Bartsch et al.(Commun Partial Differ Equ 46(9):1729--1756,2021). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_03296 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Normalized solutions on large smooth domains to the Schrödinger equations with potential and combined nonlinearities: The Sobolev critical case Lin, Xiaolu Liu, Yanjun Lv, Zongyan Analysis of PDEs In this paper, we consider the existence and multiplicity of prescribed mass solutions to the following nonlinear Schrodinger equations with mixed nonlinearities. The standard approach based on the Pohozaev identity to obtain normalized solutions is invalid as the presence of potential. Besides, Our study can be regarded as a Sobolev critical case complement of Bartsch-Qi-Zou (Math Ann 390, 4813-4859, 2024), which has addressed an open problem raised in Bartsch et al.(Commun Partial Differ Equ 46(9):1729--1756,2021). |
| title | Normalized solutions on large smooth domains to the Schrödinger equations with potential and combined nonlinearities: The Sobolev critical case |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.03296 |