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.

References in corpus (3)

• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• Uniqueness and Nondegeneracy of Ground States for $(-\Delta {)}^{s}Q+Q-Q^{\alpha +1}=0$ in $\mathbb{R}$
• Uniqueness of radial solutions for the fractional Laplacian

Cited by in corpus (3)

• Uniqueness and Nondegeneracy of positive solutions to Kirchhoff equations and its applications in singular perturbation problems
• Uniqueness and nondegeneracy of positive solutions to a class of Kirchhoff equations in ${\mathbb{R}}^3$
• Existence and asymptotic behavior of the least energy solutions for fractional Choquard equations with potential well