Abstract
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.
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