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

2024/04/01 by Oleg Asipchuk, Asipchuk, Oleg, Christopher Leonard +3 · 1 citation
Mathematics · Physics and Astronomy · #35P25 #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Dust and Plasma Wave Phenomena #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2404.01433

openalex publication_date 2024/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show the existence and stability of ground state solutions (g.s.s.) for L²-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.

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