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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, Volume 30, Issue 2, Pages 237–248
DOI: https://doi.org/10.35634/vm200207 (Mi vuu722) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Spectral properties of the Sturm–Liouville operator with a spectral parameter quadratically included in the boundary condition

L. I. Mammadovaa, I. M. Nabievbcd

a Azerbaijan State Oil and Industry University, pr. Azadlig, 20, Baku, AZ1010, Azerbaijan
b Baku State University, ul. Z. Khalilova, 23, Baku, AZ1148, Azerbaijan
c Khazar University, ul. Mahsati, 11, Baku, AZ1096, Azerbaijan
d Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, ul. B. Vahabzadeh, 9, Baku, AZ1141, Azerbaijan
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DOI: https://doi.org/10.35634/vm200207
Abstract: The article considers the Sturm–Liouville operator with a real quadratically integrable potential. Boundary conditions are non-separated. One of these boundary conditions includes the quadratic function of the spectral parameter. Some spectral properties of the operator are studied. It is proves that eigenvalues are real and non-zero and there are no associated functions to the eigenfunctions. An asymptotic formula for the spectrum of the operator is derived, and a representation of the characteristic function as an infinite product is obtained. The results of the paper play an important role in solving inverse problems of spectral analysis for differential operators.
Keywords: Sturm-Liouville operator, non-separated boundary conditions, eigenvalues, infinite product.
Funding agency Grant number
Фонд развития науки при Президенте Азербайджанской Республики EİF/MQM/Elm-Tehsil-1-2016-1(26)-71/05/1
This work was supported by the Science Development Fund of the President of the Azerbaijan Republic. Grant No. EİF/MQM/Elm-Tehsil-1-2016-1(26)-71/05/1.
Received: 07.11.2019
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: 34A30
Language: Russian
Citation: L. I. Mammadova, I. M. Nabiev, “Spectral properties of the Sturm–Liouville operator with a spectral parameter quadratically included in the boundary condition”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:2 (2020), 237–248
Citation in format AMSBIB
\Bibitem{MamNab20}
\by L.~I.~Mammadova, I.~M.~Nabiev
\paper Spectral properties of the Sturm--Liouville operator with a spectral parameter quadratically included in the boundary condition
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2020
\vol 30
\issue 2
\pages 237--248
\mathnet{http://mi.mathnet.ru/vuu722}
\crossref{https://doi.org/10.35634/vm200207}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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    References:27
     
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