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

Behrouz Emamizadeh; Amin Farjudian

Nonautonomous Dynamical Systems (2014)

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

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topBehrouz 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>.

@article{BehrouzEmamizadeh2014,

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 - Behrouz Emamizadeh

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 -

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