Normalized ground states and a mass-constrained scattering threshold for the inhomogeneous NLS with an inverse-square potential

Abstract

We study the focusing inhomogeneous nonlinear Schrödinger equation with an inverse-square potential $$i{\partial }_{t}u+\Delta u-a|x{|}^{-2}u+|x{|}^{-b}|u{|}^{\alpha }u=0,(t,x)\in \mathbb{R}\times {\mathbb{R}}^N,$$ in the mass-supercritical and energy-subcritical regime $$\frac{4-2b}{N}<\alpha <\frac{4-2b}{N-2},$$ where $N\ge 3$ and $0<b<2$. Two main lines of research have developed largely independently for this model: scattering theory below the ground-state threshold and the variational analysis of solutions with prescribed mass. In this work, we establish a connection between these two approaches.

arXiv commentThe presentation has been improved, and several comments have been added. Any further remarks or suggestions would be very welcome