It is known that ground states of the pseudo-relativistic Boson stars exist if and only if the stellar mass N > 0 satisfies N < N*, where the finite constant N* is called the critical stellar mass. Lieb and Yau conjecture in [Comm. Math. Phys., 1987] that ground states of the pseudo-relativistic Boson stars are unique for each N < N*. In this paper, we prove that the above uniqueness conjecture holds for the particular case where N > 0 is small enough. (C) 2020 Elsevier Inc. All rights reserved.
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