Adel Daoues, Amani Hammami, Kamel Saoudi
Abstract:
In this article we study a nonlocal equation involving singular and critical
Hardy-Sobolev non-linearities,
\[ \displaylines{
(-\Delta_p)^su-\mu \frac{|u|^{p-2}u}{|x|^{sp}}
=\lambda u^{-\alpha}+\frac{|u|^{p_s^*(t)-2}u}{|x|^t}, \quad\text{in }\Omega,\\
u>0,\quad\text{in }\Omega,\\
u=0,\quad\text{in }\mathbb{R}^N\setminus\Omega,
}\]
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.
DOI: https://doi.org/10.58997/ejde.2023.10
Show me the PDF file (400 KB), TEX file for this article.
 |
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 |
Return to the EJDE web page