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

Kadriye Aydemir; Oktay Mukhtarov

doi:10.53570/jnt.1018600

EN

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

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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Details

Primary Language

English

Subjects

Mathematical Sciences, Applied Mathematics

Journal Section

Research Article

Authors

Kadriye Aydemir ^*
0000-0002-8378-3949
Türkiye

Oktay Mukhtarov
0000-0001-7480-6857
Türkiye

Publication Date

December 31, 2021

Submission Date

November 3, 2021

Acceptance Date

December 28, 2021

Published in Issue

Year 2021 Number: 37

DOI

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

IZ

https://izlik.org/JA98SZ27BT

APA

Aydemir, K., & Mukhtarov, O. (2021). The Transmittal-Characteristic Function of Three-Interval Periodic Sturm-Liouville Problem with Transmission Conditions. Journal of New Theory, 37, 26-34. https://doi.org/10.53570/jnt.1018600

AMA

1.Aydemir K, Mukhtarov O. The Transmittal-Characteristic Function of Three-Interval Periodic Sturm-Liouville Problem with Transmission Conditions. JNT. 2021;(37):26-34. doi:10.53570/jnt.1018600

Chicago

Aydemir, Kadriye, and Oktay Mukhtarov. 2021. “The Transmittal-Characteristic Function of Three-Interval Periodic Sturm-Liouville Problem With Transmission Conditions”. Journal of New Theory, nos. 37: 26-34. https://doi.org/10.53570/jnt.1018600.

EndNote

Aydemir K, Mukhtarov O (December 1, 2021) The Transmittal-Characteristic Function of Three-Interval Periodic Sturm-Liouville Problem with Transmission Conditions. Journal of New Theory 37 26–34.

IEEE

[1]K. Aydemir and O. Mukhtarov, “The Transmittal-Characteristic Function of Three-Interval Periodic Sturm-Liouville Problem with Transmission Conditions”, JNT, no. 37, pp. 26–34, Dec. 2021, doi: 10.53570/jnt.1018600.

ISNAD

Aydemir, Kadriye - Mukhtarov, Oktay. “The Transmittal-Characteristic Function of Three-Interval Periodic Sturm-Liouville Problem With Transmission Conditions”. Journal of New Theory. 37 (December 1, 2021): 26-34. https://doi.org/10.53570/jnt.1018600.

JAMA

1.Aydemir K, Mukhtarov O. The Transmittal-Characteristic Function of Three-Interval Periodic Sturm-Liouville Problem with Transmission Conditions. JNT. 2021;:26–34.

MLA

Aydemir, Kadriye, and Oktay Mukhtarov. “The Transmittal-Characteristic Function of Three-Interval Periodic Sturm-Liouville Problem With Transmission Conditions”. Journal of New Theory, no. 37, Dec. 2021, pp. 26-34, doi:10.53570/jnt.1018600.

Vancouver

1.Kadriye Aydemir, Oktay Mukhtarov. The Transmittal-Characteristic Function of Three-Interval Periodic Sturm-Liouville Problem with Transmission Conditions. JNT. 2021 Dec. 1;(37):26-34. doi:10.53570/jnt.1018600