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arXiv · 2610.02933

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

Mohamed Majdoub·Tarek Saanouni
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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 $$ \frac{4-2b}{N}<α<\frac{4-2b}{N-2}, $$ 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.

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Mohamed Majdoub, Tarek Saanouni. 2026-10-02. Normalized ground states and a mass-constrained scattering threshold for the inhomogeneous NLS with an inverse-square potential. https://arxiv.org/abs/2610.02933

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