Uniqueness and Nondegeneracy of Ground States for Choquard Equations in three dimensions

Abstract

We obtain uniqueness and nondegeneracy results for ground states of Choquard equations $-\Delta u+u=\left(|x{|}^{-1}\ast |u{|}^p\right)|u{|}^{p-2}u$ in ${\mathbb{R}}^3$, provided that $p>2$ and $p$ is sufficiently close to 2.