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Saratov, Russia

Yurko V.,Saratov University
Tamkang Journal of Mathematics | Year: 2014

We study boundary value problemsoncompact graphswitha cycle for second-order ordinary differential equations with nonlinear dependence on the spectral parameter. We establish properties of the spectral characteristics and investigate inverse spectral problems of recovering coefficients of the differential equation from spectra. For these inverse problems we prove uniqueness theorems and provide procedures for constructing their solutions. Source


Yurko V.,Saratov University
Inverse Problems in Science and Engineering | Year: 2016

An inverse spectral problem is studied for differential pencils on graphs with a rooted cycle and with standard matching conditions in internal vertices. A uniqueness theorem is proved, and a constructive procedure for the solution is provided. © 2016 Taylor & Francis Source


Freiling G.,University of Duisburg - Essen | Ignatyev M.,Saratov University
Inverse Problems | Year: 2011

A scattering problem is studied for second-order differential operators on noncompact graphs with a cycle and with standard matching conditions in the internal vertices. Moreover, a uniqueness theorem for a corresponding inverse problem is proved. Problems of this type appear in various applications of mathematical physics, in particular in connection with the study of the properties of Aharonov-Bohm rings connected to one or several wires. © 2011 IOP Publishing Ltd. Source


Freiling G.,University of Duisburg - Essen | Yurko V.A.,Saratov University
Inverse Problems | Year: 2010

Sturm-Liouville differential operators in a finite interval with boundary conditions depending polynomially on the spectral parameter are studied. We establish the properties of the spectral characteristics and investigate three inverse problems of recovering the operator either from the so-called Weyl function, or from discrete spectral data or from two spectra. For these inverse problems we provide procedures for constructing their solutions by the method of spectral mappings. © 2010 IOP Publishing Ltd. Source


Ignatyev M.,Saratov University
Tamkang Journal of Mathematics | Year: 2011

A scattering problem is studied for second-order differential operator on onevertex noncompact graph with a cycle and with standardmatching conditions in the vertex. A uniqueness theorem for a corresponding inverse problem is proved and a procedure for solving the problemis provided. Source

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