Normalized ground state solutions for the fractional Sobolev critical NLSE with an extra mass supercritical nonlinearity

TL;DR

This paper establishes the existence of normalized ground state solutions for a fractional Sobolev critical nonlinear Schrödinger equation with supercritical mass, extending previous results in both local and nonlocal contexts.

Contribution

It introduces a novel technique to prove compactness of Palais-Smale sequences for the fractional Sobolev critical NLSE with supercritical nonlinearity.

Findings

Proves existence of ground state solutions

Extends known results to fractional and supercritical cases

Develops a new compactness technique

Abstract

This paper is concerned with existence of normalized ground state solutions for the mass supercritical fractional nonlinear Schr\"{o}dinger equation involving a critical growth in the fractional Sobolev sense. The compactness of Palais-Smale sequences is obtained by a special technique, which borrows from the ideas of Soave (J. Funct. Anal. 279 (6) (2020) 1086102020). This paper represents an extension of previously known results - in the local and the nonlocal cases.