Existence and non-existence of normalized solutions for a nonlinear fractional Schrödinger system
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916715508531200 |
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| author | Liu, Chungen Zhang, Zhigao Zuo, Jiabin |
| author_facet | Liu, Chungen Zhang, Zhigao Zuo, Jiabin |
| contents | This paper is concerned with a nonlinear fractional Schördinger system in $\mathbb{R}$ with intraspecies interactions $a_{i}>0 \ (i=1,2)$ and interspecies interactions $β\in\mathbb{R}$. We study this system by solving an associated constrained minimization problem (i.e., $L^2-$norm constrains). Under certain assumptions on the trapping potentials $V_i(x) \ (i=1,2),$ we derive some delicate estimates for the related energy functional and establish a criterion for the existence and non-existence of solutions, in which way several existence results are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06031 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and non-existence of normalized solutions for a nonlinear fractional Schrödinger system Liu, Chungen Zhang, Zhigao Zuo, Jiabin Analysis of PDEs 35J50, 35J61, 35Q40 This paper is concerned with a nonlinear fractional Schördinger system in $\mathbb{R}$ with intraspecies interactions $a_{i}>0 \ (i=1,2)$ and interspecies interactions $β\in\mathbb{R}$. We study this system by solving an associated constrained minimization problem (i.e., $L^2-$norm constrains). Under certain assumptions on the trapping potentials $V_i(x) \ (i=1,2),$ we derive some delicate estimates for the related energy functional and establish a criterion for the existence and non-existence of solutions, in which way several existence results are obtained. |
| title | Existence and non-existence of normalized solutions for a nonlinear fractional Schrödinger system |
| topic | Analysis of PDEs 35J50, 35J61, 35Q40 |
| url | https://arxiv.org/abs/2411.06031 |