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

Emamizadeh, Behrouz and Farjudian, Amin (2014) Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string. Nonautonomous Dynamical Systems, 1 (1). pp. 123-136. ISSN 2353-0626

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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.

Item Type: Article
Keywords: Eigenvalue problem; Ordinary differential equation; Principal eigenvalue; Monotonicity; Derivative; Symmetric rearrangements
Schools/Departments: University of Nottingham Ningbo China > Faculty of Science and Engineering > School of Computer Science
University of Nottingham Ningbo China > Faculty of Science and Engineering > School of Mathematical Sciences
Identification Number: https://doi.org/10.2478/msds-2014-0007
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Depositing User: Yu, Tiffany
Date Deposited: 28 Feb 2019 09:00
Last Modified: 28 Feb 2019 09:00
URI: http://eprints.nottingham.ac.uk/id/eprint/56192

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