Scattering of radial solutions to the inhomogeneous nonlinear Schrödinger equation

Abstract

We prove scattering below the mass–energy threshold for the focusing inhomogeneous nonlinear Schrödinger equation iut+Δu+|x|−b|u|p−1u=0,when b≥0 and N>2 in the intercritical case 0<sc<1. This work generalizes the results of Farah and Guzmán (2019), allowing a broader range of values for the parameters p and b. We use a modified version of Dodson–Murphy’s approach (Dodson and Murphy, 2017) allowing us to deal with the inhomogeneity. The proof is also valid for the classical nonlinear Schrödinger equation (b=0), extending the work in (Dodson and Murphy, 2017) for radial solutions in all intercritical cases.