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Basis Properties of Root Functions of a Vibrational Boundary Value Problem with Boundary Conditions Depending on the Spectral Parameter

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Abstract

We study the basis properties of root functions of a spectral problem describing the bending vibrations of a homogeneous rod with a longitudinal force acting in its cross sections. Both rod ends are elastically fixed and either there is a lumped mass or a follower force acts on each of the ends. We establish a sufficient condition for the basis property of the system of root functions of this problem in the space \(L_p (0, 1)\), \(1<p<\infty \), after removing two functions.

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Authors and Affiliations

  1. Baku State University, Baku, AZ1148, Azerbaijan

    Z. S. Aliyev & F. M. Namazov

  2. Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, AZ1141, Azerbaijan

    Z. S. Aliyev

Authors
  1. Z. S. Aliyev
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  2. F. M. Namazov
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Correspondence to Z. S. Aliyev or F. M. Namazov.

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Translated by V. Potapchouck

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Aliyev, Z.S., Namazov, F.M. Basis Properties of Root Functions of a Vibrational Boundary Value Problem with Boundary Conditions Depending on the Spectral Parameter. Diff Equat 56, 969–975 (2020). https://doi.org/10.1134/S0012266120080017

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  • DOI: https://doi.org/10.1134/S0012266120080017

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