On a fractional Nirenberg problem via a non-degeneracy condition

Azeb Alghanemi and Afef Rigane – GJM, Volume 6, Issue 1 (2021), 43-59.

In this paper, we establish existence results to a fractional Nirenberg problem of order $\sigma\in(0,\frac{3}{2})$ on the standard three dimensional sphere. Our approach of this paper consists of studying the limits of the non-compact orbits of the gradient flow, as did Bahri for the Nirenberg problem, and performing a Morse Lemma at infinity near these ends. This involves computing their topological contributions which then yields the results.

Categories: Issue1, 2021

Milestones:

Accepted: August 2, 2021
Published online: April 16, 2021

Authors:

Azeb Alghanemi
Department of Mathematics,
Faculty of Science King Abdulaziz University,
80230, Jeddah 21589, Saudi Arabia.
Afef Rigane
Department of Mathematics,
Faculty of Sciences of Sfax, University of Sfax,
3018 Sfax, Tunisia.