Revista de la
Unión Matemática Argentina
On a fractional Nirenberg equation: Compactness and existence results
Azeb Alghanemi and Randa Ben Mahmoud

Volume 68, no. 1 (2025), pp. 251–276    

Published online (final version): May 21, 2025

https://doi.org/10.33044/revuma.3833

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Abstract

This paper deals with a fractional Nirenberg equation of order $\sigma\in (0, n/2)$, $n\geq2$. 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.

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