Normalized solutions to critical and supercritical Schrödinger equations in a ball

Jun Wang; Zhaoyang Yin

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arXiv · 2610.04935

Normalized solutions to critical and supercritical Schrödinger equations in a ball

Jun Wang·Zhaoyang Yin

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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 $1 p_c$. Thus, in the radial class, the subcritical all masses phenomenon fails throughout the full Sobolev critical and supercritical range.

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BibTeX RIS

Jun Wang, Zhaoyang Yin. 2026-10-04. Normalized solutions to critical and supercritical Schrödinger equations in a ball. https://arxiv.org/abs/2610.04935

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