Electron. J. Diff. Equ., Vol. 2016 (2016), No. 08, pp. 1-12.

Nonhomogeneous elliptic equations involving critical Sobolev exponent and weight

Mohammed Bouchekif, Ali Rimouche

Abstract:
In this article we consider the problem
$$\displaylines{ -\hbox{div}\big(p(x)\nabla u\big)=|u|^{2^{*}-2}u+\lambda f\quad \text{in }\Omega \cr u=0 \quad \text{on }\partial\Omega }$$
where $\Omega$ is a bounded domain in $\mathbb{R}^N$, We study the relationship between the behavior of p near its minima on the existence of solutions.

Submitted June 30, 2015. Published January 6, 2016.
Math Subject Classifications: 35J20, 35J25, 35J60.
Key Words: Critical Sobolev exponent; Nehari manifold; variational principle.

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Mohammed Bouchekif
Laboratoire Systèmes Dynamiques et Applications
Faculté des Sciences
Université de Tlemcen BP 119
Tlemcen 13000, Algérie
email: m_bouchekif@yahoo.fr
Ali Rimouche
Laboratoire Systèmes Dynamiques et Applications
Faculté des Sciences
Université de Tlemcen BP 119
Tlemcen 13000, Algérie
email: ali.rimouche@mail.univ-tlemcen.dz

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