Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 21, pp. 1-17.

Title: Maximum and antimaximum principles for the p-Laplacian with weighted 
       Steklov boundary conditions

Authors: Mabel Cuesta (Univ. du Littoral, Calais, France)
         Liamidi Leadi (Univ. d'Abomey Calavi, Porto-Novo, Benin)
         Pascaline Nshimirimana (Univ. d'Abomey Calavi, Porto-Novo, Benin)

Abstract:
 We study the maximum and antimaximum principles for the p-Laplacian
 operator under Steklov boundary conditions with an indefinite weight
 $$\displaylines{ 
 -\Delta_p u + |u|^{p-2}u = 0 \quad \text{in }\Omega, \cr
 |\nabla u|^{p-2}\frac{\partial u}{\partial \nu} = \lambda m(x)|u|^{p-2}u + h(x)
 \quad\text{on }\partial\Omega,
 }$$
 where $\Omega$ is a smooth bounded domain of $\mathbb{R}^N$, N>1.
 After reviewing some elementary properties of the principal eigenvalues of
 the p-Laplacian under Steklov boundary conditions with an indefinite weight,
 we investigate the maximum and antimaximum principles for this problem.
 Also we give a characterization for the interval of the validity of the
 uniform antimaximum principle.
 
Submitted November 18, 2019. Published March 2, 2020.
Math Subject Classifications: 35J70.
Key Words: p-Laplacian; Steklov boundary conditions: indefinite weight;
           maximum and antimaximum principles.