Ground states of pseudo-relativistic boson stars under the critical stellar mass
Annales de l'I.H.P. Analyse non linéaire, Volume 34 (2017) no. 6, pp. 1611-1632.

We consider ground states of pseudo-relativistic boson stars with a self-interacting potential K(x) in R3, which can be described by minimizers of the pseudo-relativistic Hartree energy functional. Under some assumptions on K(x), minimizers exist if the stellar mass N satisfies 0<N<N, and there is no minimizer if N>N, where N is called the critical stellar mass. In contrast to the case of the Coulomb-type potential where K(x)1, we prove that the existence of minimizers may occur at N=N, depending on the local profile of K(x) near the origin. When there is no minimizer at N=N, we also present a detailed analysis of the behavior of minimizers as N approaches N from below, for which the stellar mass concentrates at a unique point.

DOI: 10.1016/j.anihpc.2017.04.001
Keywords: Ground states, Boson stars, Mass concentration, Critical mass
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Guo, Yujin; Zeng, Xiaoyu. Ground states of pseudo-relativistic boson stars under the critical stellar mass. Annales de l'I.H.P. Analyse non linéaire, Volume 34 (2017) no. 6, pp. 1611-1632. doi : 10.1016/j.anihpc.2017.04.001. http://www.numdam.org/articles/10.1016/j.anihpc.2017.04.001/

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