Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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


For citation:

Yurko V. A. On Recovering Differential Pencils on a Bush-type Graph. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2017, vol. 17, iss. 1, pp. 51-61. DOI: 10.18500/1816-9791-2017-17-1-51-61, EDN: YNBYBL

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
22.02.2017
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Russian
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517.984
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YNBYBL

On Recovering Differential Pencils on a Bush-type Graph

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

We study the inverse problem of spectral analysis for differential pencils on a bush-type graph, which is an arbitrary compact graph with one 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 Dirichlet and Neumann boundary conditions in the boundary vertices. For this class of pencils 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.

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Received: 
30.09.2016
Accepted: 
21.01.2017
Published: 
28.02.2017