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.
Categories: math-ph math.MP