Year: 2026
Type: preprint
Abstract: In this paper, we study radial normalized solutions to nonlinear Schrödinger equations in the unit ball \[ -Δu+λu=|u|^{p-1}u, \qquad \int_{B_1}|u|^2\,dx=ρ, \] where $λ$ is unknown and $p\ge p_c:=\frac{N+2}{N-2}$. Soave \cite{Soave} proved that for every $1p_c$. Thus, in the radial class, the subcritical all masses phenomenon fails throughout the full Sobolev critical and supercritical range.
Source: arXiv (Cornell University)
Authors: Wang, Jun, Yin, Zhaoyang
Institution: Sun Yat-sen University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220663319