On the uniqueness of ground states of non-local equations

TL;DR

This paper reviews a joint result on the uniqueness of ground state solutions for non-local equations involving the fractional Laplacian and offers an alternative proof for a related equation, enhancing understanding of these mathematical models.

Contribution

It presents a new proof of the uniqueness of ground states for non-local equations involving the fractional Laplacian, expanding existing theoretical frameworks.

Findings

Confirmed uniqueness of ground states for fractional Laplacian equations

Provided an alternative proof method for an intermediate long-wave equation

Enhanced theoretical understanding of non-local nonlinear equations

Abstract

We review our joint result with E. Lenzmann about the uniqueness of ground state solutions of non-linear equations involving the fractional Laplacian and provide an alternate uniqueness proof for an equation related to the intermediate long-wave equation.