Normalized solutions for the NLS equation with potential in higher dimension: the purely Sobolev critical case
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909713989369856 |
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| author | Sun, Juntao Yao, Shuai Zhang, He |
| author_facet | Sun, Juntao Yao, Shuai Zhang, He |
| contents | We study normalized solutions for the nonlinear Schrodinger (NLS) equation with potential and Sobolev critical nonlinearity. By establishing suitable assumptions on the potential, together with new techniques, we find a mountain-pass type solution for N>=6, which solves an open problem presented in a recent paper [Verzini and Yu, arXiv:2505.05357v1]. Moreover, we also find a local minimizer with negative energy for N>=3, which improves the results in [Verzini and Yu, arXiv:2505.05357v1]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23639 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normalized solutions for the NLS equation with potential in higher dimension: the purely Sobolev critical case Sun, Juntao Yao, Shuai Zhang, He Analysis of PDEs We study normalized solutions for the nonlinear Schrodinger (NLS) equation with potential and Sobolev critical nonlinearity. By establishing suitable assumptions on the potential, together with new techniques, we find a mountain-pass type solution for N>=6, which solves an open problem presented in a recent paper [Verzini and Yu, arXiv:2505.05357v1]. Moreover, we also find a local minimizer with negative energy for N>=3, which improves the results in [Verzini and Yu, arXiv:2505.05357v1]. |
| title | Normalized solutions for the NLS equation with potential in higher dimension: the purely Sobolev critical case |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.23639 |