Electron. J. Differential Equations, Vol. 2020 (2020), No. 21, pp. 1-17.

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

Mabel Cuesta, Liamidi Leadi, Pascaline Nshimirimana

Abstract:
We study the maximum and antimaximum principles for the p-Laplacian operator under Steklov boundary conditions with an indefinite weight

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.
DOI: 10.58997/ejde.2020.21

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Mabel Cuesta
Université du Littoral ULCO, LMPA
50 rue F. Buisson 62220 Calais, France
email: mabel.cuesta@univ-littoral.fr
Liamidi Leadi
Université d'Abomey Calavi, FAST, IMSP
Porto-Novo, Bénin
email: leadiare@imsp-uac.org
Pascaline Nshimirimana
Université d'Abomey Calavi, FAST, IMSP
Porto-Novo, Bénin
email: pascaline.nshimirimana@imsp-uac.org

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