Non-classical periodic boundary value problems with impulsive conditions

Sevda Nur Öztürk; Oktay Mukhtarov; Kadriye Aydemir

doi:10.54187/jnrs.1201577

EN

Non-classical periodic boundary value problems with impulsive conditions

Abstract

This study investigates some spectral properties of a new type of periodic Sturm-Liouville problem. The problem under consideration differs from the classical ones in that the differential equation is given on two disjoint segments that have a common end, and two additional interaction conditions are imposed on this common end (such interaction conditions are called various names, including transmission conditions, jump conditions, interface conditions, impulsive conditions, etc.). At first, we proved that all eigenvalues are real and there is a corresponding real-valued eigenfunction for each eigenvalue. Then we showed that two eigenfunctions corresponding to different eigenvalues are orthogonal. We also defined some left and right-hand solutions, in terms of which we constructed a new transfer characteristic function. Finally, we have defined asymptotic formulas for the transfer characteristic functions and also for the eigenvalues. The results obtained are a generalization of similar results of the classical Sturm-Liouville theory.

Keywords

Non-classical periodic boundary value problems , Eigenvalues , Eigenfunctions , Impulsive conditions

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Sevda Nur Öztürk
0000-0001-5722-3393
Türkiye

Oktay Mukhtarov
0000-0001-7480-6857
Türkiye

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

Publication Date

April 30, 2023

Submission Date

November 9, 2022

Acceptance Date

December 17, 2022

Published in Issue

Year 2023 Volume: 12 Number: 1

DOI

https://doi.org/10.54187/jnrs.1201577

IZ

https://izlik.org/JA28EP33FY

APA

Öztürk, S. N., Mukhtarov, O., & Aydemir, K. (2023). Non-classical periodic boundary value problems with impulsive conditions. Journal of New Results in Science, 12(1), 1-8. https://doi.org/10.54187/jnrs.1201577

AMA

1.Öztürk SN, Mukhtarov O, Aydemir K. Non-classical periodic boundary value problems with impulsive conditions. JNRS. 2023;12(1):1-8. doi:10.54187/jnrs.1201577

Chicago

Öztürk, Sevda Nur, Oktay Mukhtarov, and Kadriye Aydemir. 2023. “Non-Classical Periodic Boundary Value Problems With Impulsive Conditions”. Journal of New Results in Science 12 (1): 1-8. https://doi.org/10.54187/jnrs.1201577.

EndNote

Öztürk SN, Mukhtarov O, Aydemir K (April 1, 2023) Non-classical periodic boundary value problems with impulsive conditions. Journal of New Results in Science 12 1 1–8.

IEEE

[1]S. N. Öztürk, O. Mukhtarov, and K. Aydemir, “Non-classical periodic boundary value problems with impulsive conditions”, JNRS, vol. 12, no. 1, pp. 1–8, Apr. 2023, doi: 10.54187/jnrs.1201577.

ISNAD

Öztürk, Sevda Nur - Mukhtarov, Oktay - Aydemir, Kadriye. “Non-Classical Periodic Boundary Value Problems With Impulsive Conditions”. Journal of New Results in Science 12/1 (April 1, 2023): 1-8. https://doi.org/10.54187/jnrs.1201577.

JAMA

1.Öztürk SN, Mukhtarov O, Aydemir K. Non-classical periodic boundary value problems with impulsive conditions. JNRS. 2023;12:1–8.

MLA

Öztürk, Sevda Nur, et al. “Non-Classical Periodic Boundary Value Problems With Impulsive Conditions”. Journal of New Results in Science, vol. 12, no. 1, Apr. 2023, pp. 1-8, doi:10.54187/jnrs.1201577.

Vancouver

1.Sevda Nur Öztürk, Oktay Mukhtarov, Kadriye Aydemir. Non-classical periodic boundary value problems with impulsive conditions. JNRS. 2023 Apr. 1;12(1):1-8. doi:10.54187/jnrs.1201577