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Local uniqueness of ground states for rotating bose-einstein condensates with attractive interactions

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Abstract

We study ground states of two-dimensional Bose-Einstein condensates with attractive interactions in a trap V(x) rotating at the velocity \(\Omega \). It is known that there exists a critical rotational velocity \(0<\Omega ^*:=\Omega ^*(V)\le \infty \) and a critical number \(0<a^*<\infty \) such that for any rotational velocity \(0\le \Omega <\Omega ^*\), ground states exist if and only if the coupling constant a satisfies \(a<a^*\). For a general class of traps V(x), which may not be symmetric, we prove in this paper that up to a constant phase, there exists a unique ground state as \(a\nearrow a^*\), where \(\Omega \in (0,\Omega ^*)\) is fixed.

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Acknowledgements

The authors are very grateful to the referee for many valuable suggestions which lead to the great improvements of the present paper.

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  1. School of Mathematics and Statistics, and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, P.O. Box 71010, Wuhan, 430079, P. R. China

    Yujin Guo, Yong Luo & Shuangjie Peng

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  1. Yujin Guo
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  2. Yong Luo
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Correspondence to Shuangjie Peng.

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Communicated by P. H. Rabinowitz.

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Y. Guo is partially supported by NSFC under Grant No. 11931012 and also partially supported by the Fundamental Research Funds for the Central Universities (No. KJ02072020-0319)

Y. Luo is partially supported by the Project funded by China Postdoctoral Science Foundation No. 2019M662680

S. Peng is partially supported by the Key Project of NSFC under Grant No.11831009.

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Guo, Y., Luo, Y. & Peng, S. Local uniqueness of ground states for rotating bose-einstein condensates with attractive interactions. Calc. Var. 60, 237 (2021). https://doi.org/10.1007/s00526-021-02055-w

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