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.
| Original language | English |
|---|---|
| Pages (from-to) | 123-136 |
| Number of pages | 14 |
| Journal | Nonautonomous Dynamical Systems |
| Volume | 1 |
| Issue number | 1 |
| Early online date | 15 Aug 2014 |
| DOIs | |
| Publication status | Published - 15 Aug 2014 |
Keywords
- Derivative
- Eigenvalue problem
- Monotonicity
- Ordinary differential equation
- Principal eigenvalue
- Symmetric rearrangements
ASJC Scopus subject areas
- Applied Mathematics
- Analysis
- Statistics and Probability
- Numerical Analysis
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Emamizadeh, B., & Farjudian, A. (2014). Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string. Nonautonomous Dynamical Systems, 1(1), 123-136. https://doi.org/10.2478/msds-2014-0007, https://doi.org/10.2478/msds-2014-0007