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

• Autorzy: Behrouz Emamizadeh , Amin Farjudian
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Nonautonomous Dynamical Systems
• Rocznik: 2014
• Tom: 1
• Numer: 1

Daty

otrzymano

2013-12-21

zaakceptowano

2014-06-17

online

2014-08-15

Twórcy

autor

Behrouz Emamizadeh

• Department of Mathematical Sciences, University of Nottingham Ningbo China, 199 Taikang East Road, Ningbo, 315100, China

autor

Amin Farjudian

• School of Computer Science, University of Nottingham Ningbo China, 199 Taikang East Road, Ningbo, 315100, China

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Identyfikatory

DOI

10.2478/msds-2014-0007