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arXiv · 2512.01794

Solutions to Sobolev Supercritical Nonlinear Schrodinger Equations on an Annulus via a Hopf Reduction Method

Jian Liang·Hua-Yang Wang
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Abstract

This paper investigates the existence of positive solutions with a prescribed mass for nonlinear Schrodinger equations on an annulus, possibly in the Sobolev supercritical regime. A reduction method based on the Hopf fibration is used to transform the problem into a lower-dimensional one. We obtain a new mass critical threshold and we show that in the new mass subcritical or critical regimes there exists a positive solution which corresponds to a global minimizer, while in the mass supercritical regime, there exists two positive solutions which correspond to a local minimizer and a mountain pass solution respectively. Some other problems are also discussed in this paper.

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Jian Liang, Hua-Yang Wang. 2025-12-01. Solutions to Sobolev Supercritical Nonlinear Schrodinger Equations on an Annulus via a Hopf Reduction Method. https://arxiv.org/abs/2512.01794

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