Existence and multiplicity results for a fractional  curvature problem

Azeb Alghanemi; Khadijah Abdullah Sharaf; Hichem Chtioui; Mohamed Gdarat

doi:10.5802/ambp.431

Existence and multiplicity results for a fractional curvature problem

Azeb Alghanemi ¹ ; Khadijah Abdullah Sharaf ¹ ; Hichem Chtioui ² ; Mohamed Gdarat ²

¹ King Abdulaziz University Department of Mathematics Jeddah Saudi Arabia
² Sfax University Department of Mathematics Faculty of Sciences of Sfax Tunisia

Annales mathématiques Blaise Pascal, Tome 32 (2025) no. 1, pp. 1-31.

Résumé

We consider the existence problem of conformal metrics with prescribed fractional curvature on the standard sphere $S^n,n\ge 2$. It is equivalent to solving a fractional nonlinear variational equation involving a critical nonlinearity. By studying the lack of compactness of the associated variational problem, we extend the existence results of [2] and [3] to any fractional order $\sigma \in (0,\frac{n}{2})$ and prove a general existence and multiplicity Theorem under an Euler–Hopf type criterion.

Publié le : 2025-07-11

DOI : 10.5802/ambp.431

Classification : 35J60, 58E30
Keywords: Fractional nonlinear problems, Variational analysis, Critical nonlinearities, Palais–Smale condition, Critical points at infinity

Affiliations des auteurs :

Azeb Alghanemi ¹ ; Khadijah Abdullah Sharaf ¹ ; Hichem Chtioui ² ; Mohamed Gdarat ²

¹ King Abdulaziz University Department of Mathematics Jeddah Saudi Arabia
² Sfax University Department of Mathematics Faculty of Sciences of Sfax Tunisia

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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Azeb Alghanemi; Khadijah Abdullah Sharaf; Hichem Chtioui; Mohamed Gdarat. Existence and multiplicity results for a fractional  curvature problem. Annales mathématiques Blaise Pascal, Tome 32 (2025) no. 1, pp. 1-31. doi : 10.5802/ambp.431. https://ambp.centre-mersenne.org/articles/10.5802/ambp.431/

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