Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Yurko V. A. Differential operators on graphs with a cycle. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, vol. 21, iss. 3, pp. 343-351. DOI: 10.18500/1816-9791-2021-21-3-343-351, EDN: OOKLUP

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.08.2021
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English
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Article type: 
Article
UDC: 
539.374
EDN: 
OOKLUP

Differential operators on graphs with a cycle

Autors: 
Yurko Vjacheslav Anatol'evich, Saratov State University
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.

Acknowledgments: 
This work was supported in part by the Russian Foundation for Basic Research (project No. 19-01-00102).
References: 
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Received: 
26.01.2021
Accepted: 
14.03.2021
Published: 
31.08.2021