We consider ground states of pseudo-relativistic boson stars with a self-interacting potential in , which can be described by minimizers of the pseudo-relativistic Hartree energy functional. Under some assumptions on , minimizers exist if the stellar mass N satisfies , and there is no minimizer if , where is called the critical stellar mass. In contrast to the case of the Coulomb-type potential where , we prove that the existence of minimizers may occur at , depending on the local profile of near the origin. When there is no minimizer at , we also present a detailed analysis of the behavior of minimizers as N approaches from below, for which the stellar mass concentrates at a unique point.
@article{AIHPC_2017__34_6_1611_0, author = {Guo, Yujin and Zeng, Xiaoyu}, title = {Ground states of pseudo-relativistic boson stars under the critical stellar mass}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1611--1632}, publisher = {Elsevier}, volume = {34}, number = {6}, year = {2017}, doi = {10.1016/j.anihpc.2017.04.001}, zbl = {1378.85002}, mrnumber = {3712013}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2017.04.001/} }
TY - JOUR AU - Guo, Yujin AU - Zeng, Xiaoyu TI - Ground states of pseudo-relativistic boson stars under the critical stellar mass JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 1611 EP - 1632 VL - 34 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2017.04.001/ DO - 10.1016/j.anihpc.2017.04.001 LA - en ID - AIHPC_2017__34_6_1611_0 ER -
%0 Journal Article %A Guo, Yujin %A Zeng, Xiaoyu %T Ground states of pseudo-relativistic boson stars under the critical stellar mass %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 1611-1632 %V 34 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2017.04.001/ %R 10.1016/j.anihpc.2017.04.001 %G en %F AIHPC_2017__34_6_1611_0
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, Tome 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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