Work

On the CR Nirenberg problem: Density and multiplicity of solutions

Year: 2025

Type: article

Abstract: We prove some results on the density and multiplicity of positive solutions to the prescribed Webster scalar curvature problem on the [Formula: see text]-dimensional standard unit CR sphere [Formula: see text]. Specifically, we construct arbitrarily many multi-bump solutions via the variational gluing method. In particular, we show the Webster scalar curvature functions of contact forms conformal to [Formula: see text] are [Formula: see text]-dense among bounded functions which are positive somewhere. Existence results of infinitely many positive solutions to the related equation [Formula: see text] on the Heisenberg group [Formula: see text] with [Formula: see text] being asymptotically periodic with respect to left translation are also obtained. Our proofs make use of a refined analysis of bubbling behavior, gradient flow, Pohozaev identity, as well as blow up arguments.

Source: Communications in Contemporary Mathematics

DOI: 10.1142/s0219199726500197

Authors: Zhongwei Tang, Heming Wang, Bingwei Zhang

Institutions: Beijing Normal University, Chinese Academy of Sciences, Academy of Mathematics and Systems Science

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G1028838811, G4561774169, G7056448682, G8478448693