Existence of solutions for the fractional Nirenberg problem with indefinite curvature functions

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.