Existence and uniqueness of ground states for attractive Bose-Einstein condensates in box-shaped traps

作者：Li, Yan; Luo, Yong^*

来源：Journal of Mathematical Physics, 2021, 62(3): 031513.

DOI：10.1063/5.0039100

We consider ground states of two-dimensional Bose-Einstein condensates in box-shaped trapping potentials V-ext(x) with inhomogeneous attractive interactions am(x), which can be described equivalently by minimizers of Gross-Pitaevskii energy functional in bounded domains. In this paper, we prove that there is a threshold a* > 0 such that minimizers exist for 0 < a < a* and the minimizer does not exist for any a > a*. However, if a = a*, it is shown that whether minimizers exist depends sensitively on the asymptotic behaviors of m(x) near its maximum points. Moreover, based on a detailed analysis on the limit behavior of minimizers as a a*, we prove local uniqueness of minimizers under some suitable assumptions on m(x).

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