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

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