Uniqueness of normalized ground states for NLS models

TL;DR

This paper introduces two methods to establish the uniqueness of normalized ground states in nonlinear Schrödinger equations, applicable across various PDE classes, operators, domains, and nonlinearities.

Contribution

It presents novel, generalizable techniques for proving the uniqueness of normalized ground states in NLS models, expanding applicability to diverse PDEs and conditions.

Findings

Two distinct methods for proving uniqueness

Applicability to various PDE classes and operators

Framework adaptable to different domains and nonlinearities

Abstract

We present two methods to prove the uniqueness of normalized ground states. We will first discuss the key ideas and ingredients of each method. Then, we will apply them to various classes of PDEs. Our approach is applicable to other operators, domains and nonlinearities provided that some hypotheses are satisfied.