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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

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

Behrouz Emamizadeh
  • Department of Mathematical Sciences, University of Nottingham Ningbo China, 199 Taikang East Road, Ningbo, 315100, China
  • Email:
/ Amin Farjudian
  • Corresponding author
  • School of Computer Science, University of Nottingham Ningbo China, 199 Taikang East Road, Ningbo, 315100, China
  • Email:
Published Online: 2014-08-15 | DOI: https://doi.org/10.2478/msds-2014-0007

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.

Keywords: Eigenvalue problem; Ordinary differential equation; Principal eigenvalue; Monotonicity; Derivative; Symmetric rearrangements

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About the article

MCS2010: 34B60, 34L15, 34L10


Received: 2013-12-21

Accepted: 2014-06-17

Published Online: 2014-08-15



Citation Information: Nonautonomous Dynamical Systems, ISSN (Online) 2299-3193, DOI: https://doi.org/10.2478/msds-2014-0007. Export Citation

© 2014 Behrouz Emamizadeh and Amin Farjudian. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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