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

Abstract

In this paper, we investigate the following fractional Nirenberg problem: Pσg𝕊n(u) = c(n,σ)Rσḡ(x)un+2σ n−2σon𝕊n, 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.

Keywords

• Fractional Nirenberg problem
• conformal invariant operator
• variational structure
• mountain pass lemma
• blowing-up analysis method