Existence and non-existence of ground state solutions for magnetic NLS
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909157016207360 |
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| author | Asipchuk, Oleg Leonard, Christopher Zheng, Shijun |
| author_facet | Asipchuk, Oleg Leonard, Christopher Zheng, Shijun |
| contents | We show the existence and stability of ground state solutions (g.s.s.) for $L^2$-critical magnetic nonlinear Schrödinger equations (mNLS) for a class of unbounded electromagnetic potentials. We then give non-existence result by constructing a sequence of vortex type functions in the setting of RNLS with an anisotropic harmonic potential. These generalize the corresponding results in [3] and [20]. The case of an isotropic harmonic potential for rotational NLS has been recently addressed in [10]. Numerical results on the ground state profile near the threshold are also included. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_01433 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and non-existence of ground state solutions for magnetic NLS Asipchuk, Oleg Leonard, Christopher Zheng, Shijun Analysis of PDEs 35Q55, 35P25 We show the existence and stability of ground state solutions (g.s.s.) for $L^2$-critical magnetic nonlinear Schrödinger equations (mNLS) for a class of unbounded electromagnetic potentials. We then give non-existence result by constructing a sequence of vortex type functions in the setting of RNLS with an anisotropic harmonic potential. These generalize the corresponding results in [3] and [20]. The case of an isotropic harmonic potential for rotational NLS has been recently addressed in [10]. Numerical results on the ground state profile near the threshold are also included. |
| title | Existence and non-existence of ground state solutions for magnetic NLS |
| topic | Analysis of PDEs 35Q55, 35P25 |
| url | https://arxiv.org/abs/2404.01433 |