Oleg Asipchuk, Christopher Leonard, Shijun Zheng
Published 2024-04-01Version 1
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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Ground state solutions for a nonlocal equation in $\mathbb{R}^2$ involving vanishing potentials and exponential critical growth
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