Electron. J. Diff. Eqns., Vol. 2006(2006), No. 63, pp. 1-13.

Existence of solutions for some nonlinear elliptic equations

Aomar Anane, Omar Chakrone, Mohammed Chehabi

Abstract:
In this paper, we study the existence of solutions to the following nonlinear elliptic problem in a bounded subset $\Omega$ of $\mathbb{R}^{N}$:
$$\displaylines{ -\Delta _{p}u = f(x,u,\nabla u)+\mu \quad \hbox{in } \Omega ,\cr u = 0 \quad \hbox{on }\partial \Omega , }$$
where $\mu $ is a Radon measure on $\Omega $ which is zero on sets of $p$-capacity zero, $f:\Omega \times \mathbb{R}\times \mathbb{R} ^{N}\to \mathbb{R}$ is a Caratheodory function that satisfies certain conditions with respect to the one dimensional spectrum.

Submitted January 23, 2006. Published May 19,2006.
Math Subject Classifications: 35J15, 35J70, 35J85.
Key Words: Boundary value problem; truncation; p-Laplacian; spectrum.

Show me the PDF file (237K), TEX file, and other files for this article.

Aomar Anane
Departement de Mathematiques et Informatique
Faculte des Sciences
Universite Mohamed 1, Oujda, Maroc
email: anane@sciences.univ-oujda.ac.ma
Omar Chakrone
Departement de Mathematiques et Informatique
Faculte des Sciences
Universite Mohamed 1, Oujda, Maroc
email: chakrone@sciences.univ-oujda.ac.ma
Mohammed Chehabi
Departement de Mathematiques et Informatique
Faculte des Sciences
Universite Mohamed 1, Oujda, Maroc
email: chehb_md@yahoo.fr

Return to the EJDE web page