Mass concentration and uniqueness of ground states for mass subcritical rotational nonlinear Schr\"{o}dinger equations
arXiv (Cornell University)(2021)
0$ describes the strength of the attractive interactions. It is shown that ground states of the above equation can be described equivalently by minimizers of the $L^2-$ constrained variational problem. We prove that minimizers exist for any $\rho\in(0,\infty)$ when $0<\Omega<\Omega^*$, where $0<\Omega^*:=\Omega^*(V)<\infty$ denotes the critical rotational velocity of $V(x)$. While $\Omega>\Omega^*$, there admits no minimizers for any $\rho\in(0,\infty)$. For fixed $0<\Omega<\Omega^*$, by using energy estimates and blow-up analysis, we also analyze the limit behavior of minimizers as $\rho\to\infty$. Finally, we prove that up to a constant phase, there exists a unique minimizer when $\rho>0$ is large enough and $\Omega\in(0,\Omega^*)$ is fixed.
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