Electron. J. Diff. Equ., Vol. 2015 (2015), No. 69, pp. 1-11.

Nonhomogeneous elliptic problems of Kirchhoff type involving critical Sobolev exponents

Safia Benmansour, Mohammed Bouchekif

Abstract:
This article concerns the existence and the multiplicity of solutions for nonhomogeneous elliptic Kirchhoff problems involving the critical Sobolev exponent, defined on a regular bounded domain of $\mathbb{R}^3$. Our approach is essentially based on Ekeland's Variational Principle and the Mountain Pass Lemma.

Submitted December 10, 2014. Published March 24, 2015.
Math Subject Classifications: 35J20, 35J60, 47J30.
Key Words: Variational methods; critical Sobolev exponent; Nehari manifold; Palais-Smale condition; Kirchhoff equation.

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Safia Benmansour
Laboratoire des Syst èmes Dynamiques et Applications
Facult é des Sciences
Universit é de Tlemcen, BP 119
13000 Tlemcen, Alg érie
email: safiabenmansour@hotmail.fr
Mohammed Bouchekif
Laboratoire des Syst èmes Dynamiques et Applications
Facult é des Sciences
Universit é de Tlemcen, BP 119
13000 Tlemcen, Alg érie
email: m_bouchekif@yahoo.fr

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