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

Behrouz Emamizadeh, Amin Farjudian

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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.
Original languageEnglish
Pages (from-to)123-136
JournalNonautonomous Dynamical Systems
Issue number1
Early online date15 Aug 2014
Publication statusPublished Online - 15 Aug 2014


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


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