On the maximum principle for the discrete p-laplacian with sign-changing weight
Résumé
This work deals with the maximum principle for the discrete Neumann or Dirichlet problem
-Δφp(Δu(k - 1)) = λm(k)φp(u(k))+ h(k) in [1, n].
We study the existence and nonexistence of positive solution and its uniqueness.
Téléchargements
Références
A. Anane, O. Chakrone, N, Moradi, Maximum and Anti-Maximum principles for the p-Laplacian with a Nonlinear Boundary condition, Electronic Journal of Differential Equations, Conference 14 (2006) 95-107.
M. Chehabi, O.Chakrone, Properties of the First Eigenvalue with Sign-changing Weight of the Discrete p-Laplacian and Applications, Bol. Soc. Paran. Mat. (3s.) v.36 2 (2018) 151-167. https://doi.org/10.5269/bspm.v36i2.31977
H. Chehabi, O Chakrone, M. Chehabi, On the antimaximum principle for the discrete p-Laplacian with sign-changing weight, Applied Mathematics and Computation 342 (2019) 112-117. https://doi.org/10.1016/j.amc.2018.09.012
Y. Huang, On eigenvalue problems for the p-Laplacian with Neumann boundary conditions, Proc. Amer. Math. Soc. 109 (1990) 177-184. https://doi.org/10.1090/S0002-9939-1990-1010800-9
W. Allegretto, Y. Huang, A Picone's identity for the p-Laplacian and applications, Nonlinear Anal. T.M.A. 32 (1998) 819-830. https://doi.org/10.1016/S0362-546X(97)00530-0
R. L. Frank, R. Seiringer, Non-linear ground state representations and sharp Hardy inequalities, J. Funct. Anal. 255 (2008), 3407-3430. https://doi.org/10.1016/j.jfa.2008.05.015
T. Godoy, J. P. Gossez, S. Paczka, On the antimaximum principle for the p-Laplacian with indefinite weight, Nonlinear Analysis. 51 (2002) 449-467. https://doi.org/10.1016/S0362-546X(01)00839-2
T. Godoy, J. P. Gossez, S. Paczka, Antimaximum principle for elliptic problems with weight, Electr.J. Differential Equations 1999 (1999) 1-15.
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática
Ce travail est disponible sous la licence Creative Commons Attribution 4.0 International .
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
