The first eigenvalue and eigenfunction of a nonlinear elliptic system

Farid Bozorgnia; Seyyed Abbas Mohammadi; Tomáš Vejchodský

doi:10.1016/j.apnum.2019.06.004

The first eigenvalue and eigenfunction of a nonlinear elliptic system

Farid Bozorgnia (Lead / Corresponding author), Seyyed Abbas Mohammadi (Lead / Corresponding author), Tomáš Vejchodský (Lead / Corresponding author)

Mathematics

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7 Citations (Scopus)

49 Downloads (Pure)

Abstract

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, an 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.

Original language	English
Pages (from-to)	159-174
Number of pages	16
Journal	Applied Numerical Mathematics
Volume	145
Early online date	14 Jun 2019
DOIs	https://doi.org/10.1016/j.apnum.2019.06.004
Publication status	Published - Nov 2019

Keywords

Nonlinear elliptic system
p-Laplacian
Eigenvalue problem
Simplicity
Numerical approximation

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10.1016/j.apnum.2019.06.004

Submitted manuscriptSubmitted manuscript, 1.01 MBLicence: Other

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title = "The first eigenvalue and eigenfunction of a nonlinear elliptic system",

abstract = "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, an 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.",

keywords = "Nonlinear elliptic system, p-Laplacian, Eigenvalue problem, Simplicity, Numerical approximation",

author = "Farid Bozorgnia and Mohammadi, \{Seyyed Abbas\} and Tom{\'a}{\v s} Vejchodsk{\'y}",

year = "2019",

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doi = "10.1016/j.apnum.2019.06.004",

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T1 - The first eigenvalue and eigenfunction of a nonlinear elliptic system

AU - Bozorgnia, Farid

AU - Mohammadi, Seyyed Abbas

AU - Vejchodský, Tomáš

PY - 2019/11

Y1 - 2019/11

N2 - 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, an 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.

AB - 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, an 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.

KW - Nonlinear elliptic system

KW - p-Laplacian

KW - Eigenvalue problem

KW - Simplicity

KW - Numerical approximation

UR - https://www.scopus.com/pages/publications/85067361249

U2 - 10.1016/j.apnum.2019.06.004

DO - 10.1016/j.apnum.2019.06.004

M3 - Article

SN - 0168-9274

VL - 145

SP - 159

EP - 174

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

The first eigenvalue and eigenfunction of a nonlinear elliptic system

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Keywords

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The first eigenvalue and eigenfunction of a nonlinear elliptic system

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