2005-Oujda International Conference on Nonlinear Analysis,
Oujda, Morocco.
Electronic Journal of Differential Equations,
Conference 14 (2006), pp. 95-107.
Title: Maximum and anti-maximum principles for the p-Laplacian with a
nonlinear boundary condition
Authors: Aomar Anane (Univ. Mohammed 1er, Oujda, Maroc)
Omar Chakrone (Univ. Mohammed 1er, Oujda, Maroc)
Najat Moradi (Univ. Mohammed 1er, Oujda, Maroc)
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.