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Existence and non-existence of ground state solutions for magnetic NLS

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arxiv 2404.01433 v1 pith:IUFFH6UJ submitted 2024-04-01 math.AP

Oleg Asipchuk , Christopher Leonard , Shijun Zheng This is my paper · ORCID
classification math.AP
keywords groundstateexistenceharmonicmagneticnon-existencepotentialresults
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abstract

We show the existence and stability of ground state solutions (g.s.s.) for $L^2$-critical magnetic nonlinear Schr\"odinger 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.

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