Abstract
This article is devoted to studying the model of Bose-Einstein condensates (BECs) with attractive interactions, and it can be described by Gross-Pitaevskii energy functional with \(L^{2}\)–constraint for the mass. Recently, the solutions of this model concentrated at several points have been widely considered. However, it does not seem to have the result on solutions concentrating at a high dimensional subset. In this paper, we show that the existence of radial solutions of the model concentrating on spheres under suitable conditions by using modified finite dimensional reduction and blow-up analysis based on Pohozaev identity. Also we would like to point out that this concentration phenomena is quite different from those of classical nonlinear Schrödinger equations.
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Acknowledgements
Guo was supported by National Natural Science Foundation of China (No.11771469). Tian was supported by National Natural Science Foundation of China (No.11871387,12071364) and the Fundamental Research Funds for the Central Universities(WUT: 2020IA003). Zhou was supported by National Natural Science Foundation of China (No.12171183).
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Communicated by P. H. Rabinowitz.
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Guo, Q., Tian, S. & Zhou, Y. Curve-like concentration for Bose-Einstein condensates. Calc. Var. 61, 63 (2022). https://doi.org/10.1007/s00526-021-02171-7
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DOI: https://doi.org/10.1007/s00526-021-02171-7