Normalized solutions for the fractional NLS with mass supercritical nonlinearity

TL;DR

This paper studies the existence of normalized solutions to the fractional nonlinear Schrödinger equation with mass constraint, establishing ground states and multiple solutions under general nonlinearities.

Contribution

It introduces new existence and multiplicity results for normalized solutions of the fractional NLS with broad conditions on the nonlinearity.

Findings

Existence of a ground state solution.

Multiple solutions in the radially symmetric case.

Results hold under general assumptions on the nonlinearity.

Abstract

We investigate the existence of solutions to the fractional nonlinear Schr\"{o}dinger equation $(-\Delta)^s u = f(u)$ with prescribed $L^2$-norm $\int_{\mathbb{R}^N} |u|^2 \, dx =m$ in the Sobolev space $H^s(\mathbb{R}^N)$. Under fairly general assumptions on the nonlinearity $f$, we prove the existence of a ground state solution and a multiplicity result in the radially symmetric case.