Normalized solutions for the fractional NLS with mass supercritical nonlinearity

Abstract

We investigate the existence of solutions to the fractional nonlinear Schrödinger 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.