Existence of Multiple Solutions for p-Laplacian Problems Involving Critical Sobolev-Hardy Exponents and Singular Potential

Zeid I. Almuhiameed

Department of Mathematics, College of Science, Qassim University, Buraidah, KSA.

DOI: 10.4236/oalib.1106812                

Abstract

In this paper, we establish the existence of multiple solutions for p-Laplacian problems involving critical exponents and singular potential, by using Ekeland's variational principle and mountain pass theorem without Palais-Smale conditions.

Keywords

p-Laplacian Problems, Ekeland's Variational Principle, Mountain Pass Theorem, Critical Hardy-Sobolev Exponent, Singular Potential

Conflicts of Interest

The author declares no conflicts of interest regarding the publication of this paper.

References

[1]	Badiale, M. and Tarantello, G. (2002) A Sobolev-Hardy Inequality with Applications to a Nonlinear Elliptic Equation Arising in Astrophysics. Archive for Rational Mechanics and Analysis, 163, 252-293. https://doi.org/10.1007/s002050200201
[2]	Br ezis, H. and Lieb, E. (1983) A Relation Between Point Convergence of Functions and Convergence of Functional. Proceedings of the American Mathematical Society, 88, 486-490. https://doi.org/10.1090/S0002-9939-1983-0699419-3
[3]	Tarantello, G. (1992) On Nonhomogeneous Elliptic Equations Involving Critical Sobolev Exponent. Annales de lInstitut Henri Poincar e, 9, 281-304. https://doi.org/10.1016/S0294-1449(16)30238-4
[4]	Gazzini, M. and Mussina, R. (2009) On a Sobolev Type Inequality Related to the Weighted p-Laplace Operator. Journal of Mathematical Analysis and Applications, 352, 99-111.
[5]	Badiale, M., Bergio, V. and Rolando, S. (2007) A Nonlinear Elliptic Equation with Singular Potential and Applications to Nonlinear Field Equations. Journal of the European Mathematical Society, 9, 355-381.
[6]	Musina, R. (2008) Ground State Solution of a Critical Problem Involving Cylindrical Weights. Nonlinear Analysis, 68, 3972-3986.