Electron. J. Differential Equations, Vol. 2023 (2023), No. 10, pp. 1-19.

Multiplicity results of nonlocal singular PDEs with critical Sobolev-Hardy exponent

Adel Daoues, Amani Hammami, Kamel Saoudi

Abstract:
In this article we study a nonlocal equation involving singular and critical Hardy-Sobolev non-linearities,

where $\Omega \subset \mathbb{R}^N$ is a bounded domain with Lipschitz boundary and $(-\Delta_p)^s$ is the fractional p-Laplacian operator. We combine some variational techniques with a perturbation method to show the existence of multiple solutions.

Submitted November 22, 2022. Published January 26, 2023.
Math Subject Classifications: 35R11, 35J75, 35J60, 46E35.
Key Words: Nonlocal elliptic problem; singular non-linearity; variational method; Sobolev and Hardy non-linearities; perturbation method; multiple positive solutions.

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Adel Daoues
École Supérieure des Sciences et de Technologie de Hammam Sousse
Sousse, Tunisia
email: adel.daouas@essths.u-sousse.tn
Amani Hammami
École Supérieure des Sciences et de Technologie de Hammam Sousse
Sousse, Tunisia
email: amanihammami29@gmail.com
Kamel Saoudi
Basic and Applied Scientific Research Center
Imam Abdulrahman Bin Faisal University, Saudi Arabia
email: kmsaoudi@iau.edu.sa

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