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 $$i\partial_t u+Δu-a|x|^{{-2}u+|x|^{{-b}|u|^αu=0,}} \qquad (t,x)\in\mathbb{R}\times\mathbb{R}^{N},$$ in the mass-supercritical and energy-subcritical regime $$ \frac{4-2b}{N}&lt;α&lt;\frac{4-2b}{N-2}, $$ where $N\ge3$ 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.