Uniqueness of ground states for the L^2-critical boson star equation

Rupert L. Frank, Enno Lenzmann

We establish uniqueness of ground states $u(x)\ge 0$ for the $L^2$-critical boson star equation $\sqrt{-\Delta }u-(|x{|}^{-1}\ast |u{|}^2)u=-u$ in ${\mathbb{R}}^3$. The proof blends variation…