Three bound states with prescribed angular momentum to the cubic-quintic NLS equations in $\mathbb{R}^{3}$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912472736202752 |
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| author | Yao, Shuai Sun, Juntao |
| author_facet | Yao, Shuai Sun, Juntao |
| contents | In this paper, we investigate bound states with prescribed angular momentum and mass for the nonlinear Schrödinger equations (NLS) with the cubic-quintic nonlinearity in dimensions three. We demonstrate that there exist three solutions for the double constrained problem: a local minimizer, a mountain pass type solution, and a global minimizer. Moreover, by means of the minimax method, we construct a new mountain pass path and further obtain the geometric link among the three solutions as well as a comparison of their energy levels. This seems to be the first paper concerning three solutions, with the method also being applicable to the single constraint problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04057 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Three bound states with prescribed angular momentum to the cubic-quintic NLS equations in $\mathbb{R}^{3}$ Yao, Shuai Sun, Juntao Analysis of PDEs In this paper, we investigate bound states with prescribed angular momentum and mass for the nonlinear Schrödinger equations (NLS) with the cubic-quintic nonlinearity in dimensions three. We demonstrate that there exist three solutions for the double constrained problem: a local minimizer, a mountain pass type solution, and a global minimizer. Moreover, by means of the minimax method, we construct a new mountain pass path and further obtain the geometric link among the three solutions as well as a comparison of their energy levels. This seems to be the first paper concerning three solutions, with the method also being applicable to the single constraint problem. |
| title | Three bound states with prescribed angular momentum to the cubic-quintic NLS equations in $\mathbb{R}^{3}$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.04057 |