On the maximum principle for the discrete p-laplacian with sign-changing weight
Resumen
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.
Descargas
Citas
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.
Derechos de autor 2022 Boletim da Sociedade Paranaense de Matemática

Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
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).