Spectrum of the Non-self-adjoint and Non-homogeneous Sturm-Liouville Operators with a Singular Potential

Cem Koşar; Nida Palamut Koşar

doi:10.29132/ijpas.1908033

Spectrum of the Non-self-adjoint and Non-homogeneous Sturm-Liouville Operators with a Singular Potential

Abstract

In this paper we discuss in detail the quantitative properties of the spectrum of the non-self-adjoint and non-homogeneous Sturm Liouville Operators with a singular potential. The problem is formulated on the half-line and is supplemented by a boundary condition imposed at the origin, which reflects and accommodates the singular nature of the potential term. Special attention is given to the analytical structure of the spectrum under these conditions. In particular, we study the eigenvalues and spectral singularities in depth and establish a robust sufficient condition ensuring the finiteness of the eigenvalues, spectral singularities, and their respective multiplicities with this operator theoretic framework.

Keywords

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Ethical Statement

The author(s) declare that they have complied with the scientific, ethical, and citation rules of the International Journal of Pure and Applied Sciences throughout all stages of the study.

Thanks

The author(s) sincerely thank the reviewers and the editorial board of the International Journal of Pure and Applied Sciences for their valuable comments and suggestions.

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Cem Koşar
0000-0003-4949-4956
Türkiye

Nida Palamut Koşar ^*
0000-0003-2421-7872
Türkiye

Publication Date

June 22, 2026

Submission Date

March 11, 2026

Acceptance Date

May 26, 2026

Published in Issue

Year 2026 Volume: 12 Number: 1

DOI

https://doi.org/10.29132/ijpas.1908033

IZ

https://izlik.org/JA74CA83AE

Cite

RIS / Bibtex

APA

Koşar, C., & Palamut Koşar, N. (2026). Spectrum of the Non-self-adjoint and Non-homogeneous Sturm-Liouville Operators with a Singular Potential. International Journal of Pure and Applied Sciences, 12(1), 335-343. https://doi.org/10.29132/ijpas.1908033

AMA

1.Koşar C, Palamut Koşar N. Spectrum of the Non-self-adjoint and Non-homogeneous Sturm-Liouville Operators with a Singular Potential. International Journal of Pure and Applied Sciences. 2026;12(1):335-343. doi:10.29132/ijpas.1908033

Chicago

Koşar, Cem, and Nida Palamut Koşar. 2026. “Spectrum of the Non-Self-Adjoint and Non-Homogeneous Sturm-Liouville Operators With a Singular Potential”. International Journal of Pure and Applied Sciences 12 (1): 335-43. https://doi.org/10.29132/ijpas.1908033.

EndNote

Koşar C, Palamut Koşar N (June 1, 2026) Spectrum of the Non-self-adjoint and Non-homogeneous Sturm-Liouville Operators with a Singular Potential. International Journal of Pure and Applied Sciences 12 1 335–343.

IEEE

[1]C. Koşar and N. Palamut Koşar, “Spectrum of the Non-self-adjoint and Non-homogeneous Sturm-Liouville Operators with a Singular Potential”, International Journal of Pure and Applied Sciences, vol. 12, no. 1, pp. 335–343, June 2026, doi: 10.29132/ijpas.1908033.

ISNAD

Koşar, Cem - Palamut Koşar, Nida. “Spectrum of the Non-Self-Adjoint and Non-Homogeneous Sturm-Liouville Operators With a Singular Potential”. International Journal of Pure and Applied Sciences 12/1 (June 1, 2026): 335-343. https://doi.org/10.29132/ijpas.1908033.

JAMA

1.Koşar C, Palamut Koşar N. Spectrum of the Non-self-adjoint and Non-homogeneous Sturm-Liouville Operators with a Singular Potential. International Journal of Pure and Applied Sciences. 2026;12:335–343.

MLA

Koşar, Cem, and Nida Palamut Koşar. “Spectrum of the Non-Self-Adjoint and Non-Homogeneous Sturm-Liouville Operators With a Singular Potential”. International Journal of Pure and Applied Sciences, vol. 12, no. 1, June 2026, pp. 335-43, doi:10.29132/ijpas.1908033.

Vancouver

1.Cem Koşar, Nida Palamut Koşar. Spectrum of the Non-self-adjoint and Non-homogeneous Sturm-Liouville Operators with a Singular Potential. International Journal of Pure and Applied Sciences. 2026 Jun. 1;12(1):335-43. doi:10.29132/ijpas.1908033