Lower bounds on the eigenvalue ratio with Robin boundary conditions

We study the problem of minimizing the ratio of the first eigenvalues of vibrating string equations subject to the Robin boundary conditions for the class of concave weights. We show that, unlike the Dirichlet, Neumann and mixed boundary conditions, the constant weight is not minimizing for the clas...

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Bibliographic Details
Published inGulf Journal of Mathematics Vol. 19; no. 2; pp. 489 - 499
Main Authors Ahrami, Mohammed, Zakaria El Allali, Jamal Ounejma
Format Journal Article
LanguageEnglish
Published 30.04.2025
Online AccessGet full text
ISSN2309-4966
2309-4966
DOI10.56947/gjom.v19i2.2825

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Summary:We study the problem of minimizing the ratio of the first eigenvalues of vibrating string equations subject to the Robin boundary conditions for the class of concave weights. We show that, unlike the Dirichlet, Neumann and mixed boundary conditions, the constant weight is not minimizing for the class of concave weights. In addition, we prove a relation between the eigenvalues and real roots of the first Airy functions and their derivatives.
ISSN:2309-4966
2309-4966
DOI:10.56947/gjom.v19i2.2825