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Original scientific paper

A family of isospectral fourth order Sturm Liouville problems and equivalent beam equations Hanif Mirzaei

Hanif Mirzaei ; Department of Mathematics, Sahand University of Technology, Tabriz, Iran


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Abstract

In this paper, we consider the class of fourth order Sturm- Liouville equation of the form y(4)(z)2(q(z)y)+(q2(z)q(z))y(z)=λ2y(z), 0zL, with boundary conditions y(z)=y(z)=0 at z=0,L. We prove that this class is equivalent to a second order Sturm Liouville problem. Using Darboux Lemma we obtain the closed form of fourth order Sturm-Liouville equations that is isospectral to a given one. Also we obtain the Euler Bernoulli beam equation equivalent to this class.

Keywords

Isospectral; fourth order Sturm-Liouville equation; Euler-Bernoulli beam equation

Hrčak ID:

192105

URI

https://hrcak.srce.hr/192105

Publication date:

30.5.2018.

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