The first eigenvalue and eigenfunction of a nonlinear elliptic system

In this paper, we study the first eigenvalue of a nonlinear elliptic system involving \(p\)-Laplacian as the differential operator. The principal eigenvalue of the system and the corresponding eigenfunction are investigated both analytically and numerically. An alternative proof to show the simplici...

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Bibliographic Details
Published in:arXiv.org 2019-05
Main Authors: Bozorgnia, Farid, Seyyed Abbas Mohammadi, Vejchodsky, Tomas
Format: Article
Language:English
Subjects:
Algorithms
Differential equations
Eigenvalues
Eigenvectors
Lower bounds
Numerical analysis
Operators (mathematics)
Online Access:Get full text
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Summary:In this paper, we study the first eigenvalue of a nonlinear elliptic system involving \(p\)-Laplacian as the differential operator. The principal eigenvalue of the system and the corresponding eigenfunction are investigated both analytically and numerically. An alternative proof to show the simplicity of the first eigenvalue is given. In addition, the upper and lower bounds of the first eigenvalue are provided. Then, a numerical algorithm is developed to approximate the principal eigenvalue. This algorithm generates a decreasing sequence of positive numbers and various examples numerically indicate its convergence. Further, the algorithm is generalized to a class of gradient quasilinear elliptic systems.
ISSN:2331-8422