Nonradial normalized solutions for a quasilinear Schrödinger equation via dual approach
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915483004960768 |
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| author | Zhang, Lin |
| author_facet | Zhang, Lin |
| contents | In this paper, we will utilize the dual method to construct multiple nonradial normalized solutions of the following quasilinear Schrödinger equation: \begin{equation*} -Δu-Δ(|u|^{2})u-μu=|u|^{p-2}u, \qquad in \quad \mathbb{R}^N, \end{equation*} subject to a mass-subcritical constraint. It should be emphasized that the nonradial result of this equation is new. Besides that, when considering the nonradial problem, it is necessary to construct a new workspace to ensure the compactness. Meanwhile, in this paper, we will expand on the method mentioned in TMNA. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05557 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonradial normalized solutions for a quasilinear Schrödinger equation via dual approach Zhang, Lin Analysis of PDEs 35B38, 35J62 In this paper, we will utilize the dual method to construct multiple nonradial normalized solutions of the following quasilinear Schrödinger equation: \begin{equation*} -Δu-Δ(|u|^{2})u-μu=|u|^{p-2}u, \qquad in \quad \mathbb{R}^N, \end{equation*} subject to a mass-subcritical constraint. It should be emphasized that the nonradial result of this equation is new. Besides that, when considering the nonradial problem, it is necessary to construct a new workspace to ensure the compactness. Meanwhile, in this paper, we will expand on the method mentioned in TMNA. |
| title | Nonradial normalized solutions for a quasilinear Schrödinger equation via dual approach |
| topic | Analysis of PDEs 35B38, 35J62 |
| url | https://arxiv.org/abs/2509.05557 |