Multiple Solutions for Elliptic Problem with Singular Cylindrical Potential and Critical ExponentMohammed El Mokhtar Ould El Mokhtar*
Qassim University, College of Science, Departement of Mathematics, BO 6644, Bu- raidah: 51452, Kingdom of Saudi Arabia
- *Corresponding Author:
- Mohammed El Mokhtar Ould El Mokhtar
Qassim University, College of Science
Departement of Mathematics
BO 6644, Bu- raidah: 51452
Kingdom of Saudi Arabia
Tel: +966 16 380 0050
E-mail: [email protected]
Received Date: August 08, 2015; Accepted Date: December 11, 2015; Published Date: January 10, 2016
Citation : Ould El Mokhtar MEM (2016) Multiple Solutions for Elliptic Problem with Singular Cylindrical Potential and Critical Exponent. J Inform Tech Softw Eng 6:166. doi:10.4172/2165-7866.1000166
Copyright: © 2016 Ould El Mokhtar MEM. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
In the present paper, a quasilinear elliptic problem with singular cylindrical potential and critical exponent, is considered. By using the Nehari manifold and mountain pass theorem, the existence of at least four distinct solutions is obtained. The result depends crucially on the parameters a, b, m, s, λ and μ.