2005-Oujda International Conference on Nonlinear Analysis, Oujda, Morocco.
Electron. J. Diff. Eqns., Conference 14 (2006), pp. 95-107.

Maximum and anti-maximum principles for the p-Laplacian with a nonlinear boundary condition

Aomar Anane, Omar Chakrone, Najat Moradi

Abstract:
In this paper we study the maximum and the anti-maximum principles for the problem $\Delta _{p}u=|u|^{p-2}u$ in the bounded smooth domain $\Omega \subset \mathbb{R}^{N}$, with $|\nabla u|^{p-2}\frac{\partial u}{\partial \nu }=\lambda |u|^{p-2}u+h$ as a non linear boundary condition on $\partial \Omega $ which is supposed $C^{2\beta }$ for some $\beta $ in $]0,1[$, and where $h\in L^{\infty }(\partial \Omega )$. We will also examine the existence and the non existence of the solutions and their signs.

Published September 20, 2006.
Math Subject Classifications: 35J65, 35J25.
Key Words: Anti-maximum; p-laplacian; non linear boundary condition.

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Aomar Anane
Département de Mathématiques et Informatique
Faculté des Sciences
Université Mohammed 1er, Oujda, Maroc
email: anane@sciences.univ-oujda.ac.ma
Omar Chakrone
Département de Mathématiques et Informatique
Faculté des Sciences
Université Mohammed 1er, Oujda, Maroc
email: chakrone@sciences.univ-oujda.ac.ma
  Najat Moradi
Département de Mathématiques et Informatique
Faculté des Sciences
Université Mohammed 1er, Oujda, Maroc
email: najat_moradi@yahoo.fr

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