Cuesta, MabelLeadi, LiamidiNshimirimana, Pascaline2021-09-212021-09-212020-03-02Cuesta, M., Leadi, L., & Nshimirimana, P. (2020). Maximum and antimaximum principles for the p-Laplacian with weighted Steklov boundary conditions. <i>Electronic Journal of Differential Equations, 2020</i>(21), pp. 1-17.1072-6691https://hdl.handle.net/10877/14525We study the maximum and antimaximum principles for the p-Laplacian operator under Steklov boundary conditions with an indefinite weight -Δpu + |u|p-2 u = 0 in Ω, |∇u|p-2 ∂u/∂v = λm(x)|u|p-2 u + h(x) on ∂Ω, where Ω is a smooth bounded domain of ℝN, 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.Text17 pages1 file (.pdf)enAttribution 4.0 Internationalp-LaplacianSteklov boundary conditionsIndefinite weightMaximum and antimaximum principlesArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.