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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, Volume 21, Issue 3, Pages 343–351
DOI: https://doi.org/10.18500/1816-9791-2021-21-3-343-351
(Mi isu900)
 

This article is cited in 1 scientific paper (total in 1 paper)

Scientific Part
Mathematics

Differential operators on graphs with a cycle

V. A. Yurko

Saratov State University, 83 Astrakhanskaya St., Saratov 410012, Russia
Full-text PDF (159 kB) Citations (1)
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Abstract: An inverse problem of spectral analysis is studied for Sturm – Liouville differential operators on a graph with a cycle. We pay the main attention to the most important nonlinear inverse problem of recovering coefficients of differential equations provided that the structure of the graph is known a priori. We use the standard matching conditions in the interior vertices and Robin boundary conditions in the boundary vertices. For this class of operators properties of spectral characteristics are established, a constructive procedure is obtained for the solution of the inverse problem of recovering coefficients of differential operators from spectra, and the uniqueness of the solution is proved. For solving this inverse problem we use the method of spectral mappings, which allows one to construct the potential on each fixed edge. For transition to the next edge we use a special representation of the characteristic functions.
Key words: Sturm – Liouville operators, geometrical graphs, inverse spectral problems.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00102
This work was supported in part by the Russian Foundation for Basic Research (project No. 19-01-00102).
Received: 26.01.2021
Accepted: 14.03.2021
Bibliographic databases:
Document Type: Article
UDC: 539.374
Language: English
Citation: V. A. Yurko, “Differential operators on graphs with a cycle”, Izv. Saratov Univ. Math. Mech. Inform., 21:3 (2021), 343–351
Citation in format AMSBIB
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\by V.~A.~Yurko
\paper Differential operators on graphs with a cycle
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2021
\vol 21
\issue 3
\pages 343--351
\mathnet{http://mi.mathnet.ru/isu900}
\crossref{https://doi.org/10.18500/1816-9791-2021-21-3-343-351}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000692198400007}
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  • https://www.mathnet.ru/eng/isu/v21/i3/p343
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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    Full-text PDF :51
    References:30
     
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