Resumen de On a fractional Nirenberg equation: Compactness and existence results

Azeb Alghanemi, Randa Ben Mahmoud

• This paper deals with a fractional Nirenberg equation of order σ ∈ (0, n/2), n ≥ 2. We study the compactness defect of the associated variational problem. We determine precise characterizations of critical points at infinity of the problem, through the construction of a suitable pseudo-gradient at infinity. Such a construction requires detailed asymptotic expansions of the associated energy functional and its gradient. This study will then be used to derive new existence results for the equation.