# Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string

• Volume: 1, Issue: 1, page 123-136, electronic only
• ISSN: 2353-0626

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## Abstract

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In this paper we consider a parametric eigenvalue problem related to a vibrating string which is constructed out of two different materials. Using elementary analysis we show that the corresponding principal eigenvalue is increasing with respect to the parameter. Using a rearrangement technique we recapture a part of our main result, in case the difference between the densities of the two materials is sufficiently small. Finally, a simple numerical algorithm will be presented which will also provide further insight into the dynamics of the non-principal eigenvalues of the system.

## How to cite

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Behrouz Emamizadeh, and Amin Farjudian. "Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string." Nonautonomous Dynamical Systems 1.1 (2014): 123-136, electronic only. <http://eudml.org/doc/266723>.

abstract = {In this paper we consider a parametric eigenvalue problem related to a vibrating string which is constructed out of two different materials. Using elementary analysis we show that the corresponding principal eigenvalue is increasing with respect to the parameter. Using a rearrangement technique we recapture a part of our main result, in case the difference between the densities of the two materials is sufficiently small. Finally, a simple numerical algorithm will be presented which will also provide further insight into the dynamics of the non-principal eigenvalues of the system.},
author = {Behrouz Emamizadeh, Amin Farjudian},
journal = {Nonautonomous Dynamical Systems},
keywords = {Eigenvalue problem; Ordinary differential equation; Principal eigenvalue; Monotonicity; Derivative; Symmetric rearrangements; eigenvalue problem; ordinary differential equation; principal eigenvalue; monotonicity; derivative; symmetric rearrangements},
language = {eng},
number = {1},
pages = {123-136, electronic only},
title = {Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string},
url = {http://eudml.org/doc/266723},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Amin Farjudian
TI - Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string
JO - Nonautonomous Dynamical Systems
PY - 2014
VL - 1
IS - 1
SP - 123
EP - 136, electronic only
AB - In this paper we consider a parametric eigenvalue problem related to a vibrating string which is constructed out of two different materials. Using elementary analysis we show that the corresponding principal eigenvalue is increasing with respect to the parameter. Using a rearrangement technique we recapture a part of our main result, in case the difference between the densities of the two materials is sufficiently small. Finally, a simple numerical algorithm will be presented which will also provide further insight into the dynamics of the non-principal eigenvalues of the system.
LA - eng
KW - Eigenvalue problem; Ordinary differential equation; Principal eigenvalue; Monotonicity; Derivative; Symmetric rearrangements; eigenvalue problem; ordinary differential equation; principal eigenvalue; monotonicity; derivative; symmetric rearrangements
UR - http://eudml.org/doc/266723
ER -

## References

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