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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 23, Issue 6


Inverse problems for variable order differential operators with regular singularities on graphs

Vjacheslav A. Yurko
Published Online: 2015-05-23 | DOI: https://doi.org/10.1515/jiip-2014-0085


We study inverse spectral problems for ordinary differential equations with regular singularities on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.

Keywords: Geometrical graphs; differential operators; regular singularities; inverse spectral problems

MSC: 34A55; 34L05; 47E05

About the article

Received: 2014-12-08

Revised: 2015-02-11

Accepted: 2015-02-20

Published Online: 2015-05-23

Published in Print: 2015-12-01

Funding Source: Russian Ministry of Education and Science

Award identifier / Grant number: 1.1436.2014K

Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 13-01-00134

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 23, Issue 6, Pages 647–656, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2014-0085.

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