On a fractional Nirenberg equation: Compactness and existence results

• Azeb Alghanemi ^[1] ; Randa Ben Mahmoud ^[2]
  1. [1] King Abdulaziz University

     King Abdulaziz University

     Arabia Saudí

     
  2. [2] University of Sfax

     University of Sfax

     Túnez

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 68, Nº. 1, 2025, págs. 251-276
• Idioma: inglés
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• Resumen

  • 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.