On a fractional Nirenberg type problem on the n-dimensional sphere

Abstract

In this paper, we study a fractional Nirenberg type problem involving the fractional Laplacian on the standard n-dimensional sphere, . We describe the lack of compactness of the associated variational problem and we give an existence result generalizing the one given by T. Jin, Y. Li and J. Xiong. Our method hinges on a readapted characterization of critical points at infinity techniques introduced by A. Bahri and Bahri–Coron.

Keywords:

• Fractional Laplacian
• critical exponent
• critical points at infinity

AMS Subject Classifications:

• 35J60
• 35B33
• 35B99
• 35R11
• 58E30

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under [grant number 130-655-D1435]. The authors, therefore, gratefully acknowledge the DSR technical and financial support.