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

• Main Authors: Aomar Anane, Omar Chakrone, Najat Moradi
• Format: Article
• Language: English
• Published: Texas State University 2006-09-01
• Series: Electronic Journal of Differential Equations
• Subjects: Anti-maximum; p-laplacian; non linear boundary condition.
• Online Access: http://ejde.math.txstate.edu/conf-proc/14/a8/abstr.html

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 $|abla u|^{p-2}frac{partial u}{partial u }=lambda |u|^{p-2}u+h$ as a non linear boundary condition on $partial Omega $ which is supposed $C^{2eta }$ for some $eta $ in $]0,1[$, and where $hin L^{infty }(partial Omega )$. We will also examine the existence and the non existence of the solutions and their signs.