Study on the Basis Properties of Eigenfunctions for Differential Problems with Conjugation

Gulsum Allahyar Aghayeva; Alirza Akhmedov; Davron Juraev

doi:10.33401/fujma.1932578

Study on the Basis Properties of Eigenfunctions for Differential Problems with Conjugation

Abstract

This paper investigates the spectral properties of a second-order differential operator with a discontinuity point and conjugation conditions containing a spectral parameter. The analysis is carried out within the framework of functional analysis and basis theory in Banach and Hilbert spaces. Sufficient conditions are established for the completeness, minimality, and basis properties of the system of eigenfunctions and associated functions. It is proved that the root functions form a basis in the corresponding Lebesgue spaces and a Riesz basis in the Hilbert space setting. The obtained results provide a rigorous characterization of spectral expansions and contribute to the theory of discontinuous differential operators with nonclassical conjugation conditions.

Keywords

Ethical Statement

This article does not contain any studies with human or animal subjects.

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Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems

Journal Section

Research Article

Authors

Gulsum Allahyar Aghayeva
0000-0002-7246-5902
Azerbaijan

Alirza Akhmedov
0000-0001-7768-0049
Azerbaijan

Davron Juraev ^*
0000-0003-1224-6764
Uzbekistan

Publication Date

June 30, 2026

Submission Date

April 17, 2026

Acceptance Date

June 29, 2026

Published in Issue

Year 2026 Volume: 9 Number: 2

DOI

https://doi.org/10.33401/fujma.1932578

IZ

https://izlik.org/JA99ZR64UJ

Cite

RIS / Bibtex

APA

Aghayeva, G. A., Akhmedov, A., & Juraev, D. (2026). Study on the Basis Properties of Eigenfunctions for Differential Problems with Conjugation. Fundamental Journal of Mathematics and Applications, 9(2), 102-112. https://doi.org/10.33401/fujma.1932578

AMA

1.Aghayeva GA, Akhmedov A, Juraev D. Study on the Basis Properties of Eigenfunctions for Differential Problems with Conjugation. Fundam. J. Math. Appl. 2026;9(2):102-112. doi:10.33401/fujma.1932578

Chicago

Aghayeva, Gulsum Allahyar, Alirza Akhmedov, and Davron Juraev. 2026. “Study on the Basis Properties of Eigenfunctions for Differential Problems With Conjugation”. Fundamental Journal of Mathematics and Applications 9 (2): 102-12. https://doi.org/10.33401/fujma.1932578.

EndNote

Aghayeva GA, Akhmedov A, Juraev D (June 1, 2026) Study on the Basis Properties of Eigenfunctions for Differential Problems with Conjugation. Fundamental Journal of Mathematics and Applications 9 2 102–112.

IEEE

[1]G. A. Aghayeva, A. Akhmedov, and D. Juraev, “Study on the Basis Properties of Eigenfunctions for Differential Problems with Conjugation”, Fundam. J. Math. Appl., vol. 9, no. 2, pp. 102–112, June 2026, doi: 10.33401/fujma.1932578.

ISNAD

Aghayeva, Gulsum Allahyar - Akhmedov, Alirza - Juraev, Davron. “Study on the Basis Properties of Eigenfunctions for Differential Problems With Conjugation”. Fundamental Journal of Mathematics and Applications 9/2 (June 1, 2026): 102-112. https://doi.org/10.33401/fujma.1932578.

JAMA

1.Aghayeva GA, Akhmedov A, Juraev D. Study on the Basis Properties of Eigenfunctions for Differential Problems with Conjugation. Fundam. J. Math. Appl. 2026;9:102–112.

MLA

Aghayeva, Gulsum Allahyar, et al. “Study on the Basis Properties of Eigenfunctions for Differential Problems With Conjugation”. Fundamental Journal of Mathematics and Applications, vol. 9, no. 2, June 2026, pp. 102-1, doi:10.33401/fujma.1932578.

Vancouver

1.Gulsum Allahyar Aghayeva, Alirza Akhmedov, Davron Juraev. Study on the Basis Properties of Eigenfunctions for Differential Problems with Conjugation. Fundam. J. Math. Appl. 2026 Jun. 1;9(2):102-1. doi:10.33401/fujma.1932578