Existence and uniqueness of ground states for $p$ - Choquard model in 3D

TL;DR

This paper proves the existence and uniqueness of ground states for the 3D p-Choquard equation by leveraging radial symmetry, Pohozaev identities, and Gronwall lemma, contributing to the mathematical understanding of this nonlinear model.

Contribution

It establishes the first rigorous proof of existence and uniqueness of ground states for the 3D p-Choquard equation using novel analytical techniques.

Findings

Existence of ground states is confirmed.

Uniqueness of ground states is established.

Radial symmetry simplifies the problem to an ODE system.

Abstract

We study the $p$-Choquard equation in 3-dimensional case and establish existence and uniqueness of ground states for the corresponding Weinstein functional. For proving the uniqueness of ground states, we use the radial symmetry to transform the equation into an ordinary differential system, and applying the Pohozaev identities and Gronwall lemma we show that any two Weinstein minimizers coincide.