The Transmittal-Characteristic Function of Three-Interval Periodic Sturm-Liouville Problem with Transmission Conditions

Year 2021, Issue: 37, 26 - 34, 31.12.2021

Kadriye Aydemir Oktay Mukhtarov

https://doi.org/10.53570/jnt.1018600

Abstract

In this paper, we study the periodic Sturm-Liouville problem, defined on three non-intersecting intervals with four supplementary conditions which are imposed at two internal points of interaction, the so-called
transmission conditions. We first prove that the eigenvalues are real and the system of eigenfunctions is an orthogonal system. Secondly, some auxiliary initial-value problems are defined and transmittal-characteristic function is constructed in terms of solutions of these initial-value problems. Finally, we
establish that the eigenvalues of the considered problem are the zeros of the transmittal-characteristic function.

Keywords

Periodic transmittal Sturm-Liouville problem, characteristic function, spectrum

Supporting Institution

Amasya University

Project Number

FMB-BAP 20-0440

Thanks

This work was supported by the Office of Scientific Research Projects Coordination at Amasya University, Grant number: FMB-BAP 20-0440.

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