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

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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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Official URL: https://www.degruyter.com/dg/viewarticle/j$002fmsds.2014.1.issue-1$002fmsds-2014-0007$002fmsds-2014-0007.xml

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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