Existence of solutions for the fractional Nirenberg problem with indefinite curvature functions
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Published:2024-07-10
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Volume:
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ISSN:1664-3607
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Container-title:Bulletin of Mathematical Sciences
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language:en
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Short-container-title:Bull. Math. Sci.
Author:
An Jiaxing1ORCID,
Dou Jingbo1ORCID,
Hu Yunyun1ORCID
Affiliation:
1. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, Shaanxi, 710119, P. R. China
Abstract
In this paper, we investigate the following fractional Nirenberg problem: [Formula: see text] where [Formula: see text] is fractional order conformal invariant operator and [Formula: see text] is the [Formula: see text]-curvature for [Formula: see text] with [Formula: see text] with [Formula: see text] and [Formula: see text]. We show the existence results to the above equation employing the variational method and blowing-up analysis method, when the rotationally symmetric and indefinite curvature function [Formula: see text] satisfies certain flatness conditions.
Funder
National Natural Science Foundation of China
Youth Innovation Team of Shaanxi Universities, Shaanxi Fundamental Science Research Project for Mathematics and Physics
Fundamental Research Funds for the Central Universities
Publisher
World Scientific Pub Co Pte Ltd