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On the spectrum of a multipoint boundary value problem for a fourth-order equation

On the spectrum of a multipoint boundary value problem for a fourth-order equation We study the spectral properties of a multipoint boundary value problem for a fourth-order equation that describes small deformations of a chain of rigidly connected rods with elastic supports. We study the dependence of the spectrum of the boundary value problem on the rigidity coefficients of the supports. We show that the spectrum of the boundary value problem splits into two parts, one of which is movable under changes of the rigidity coefficients and the other remains fixed. As the rigidity coefficients grow, the eigenvalues corresponding to the movable part of the spectrum grow as well; moreover, the double degeneration of some eigenvalues is possible. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On the spectrum of a multipoint boundary value problem for a fourth-order equation

Kulaev, R.
Differential Equations , Volume 52 (3) – May 11, 2016
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References (22)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S001226611603006X
Publisher site
See Article on Publisher Site

Abstract

We study the spectral properties of a multipoint boundary value problem for a fourth-order equation that describes small deformations of a chain of rigidly connected rods with elastic supports. We study the dependence of the spectrum of the boundary value problem on the rigidity coefficients of the supports. We show that the spectrum of the boundary value problem splits into two parts, one of which is movable under changes of the rigidity coefficients and the other remains fixed. As the rigidity coefficients grow, the eigenvalues corresponding to the movable part of the spectrum grow as well; moreover, the double degeneration of some eigenvalues is possible.

Journal

Differential Equations – Springer Journals

Published: May 11, 2016

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