Existence of solutions to perturbed fractional Nirenberg problems

Abstract

In this article we study a fractional Nirenberg problem with a small perturbation of a constant. Under a flatness assumption around the critical points, we prove an existence result in terms of Euler-Hopf index. Our method hinges on a revisited version of the celebrated critical points at infinity approach which goes back to Bahri.

Keywords

• Fractional Laplacian
• critical exponent
• sigma-curvature
• critical points at infinity