Izvestiya of Saratov University.
Mathematics. Mechanics. Informatics
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

inverse spectral problems

Differential operators on graphs with a cycle

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.

On Determination of Functional-Differential Pencils on Closed Sets from the Weyl-Type Function

Second-order functional-differential pencils on closed sets are considered with nonlinear dependence on the spectral parameter. Properties of their spectral characteristics are obtained and the inverse problem is studied, which consists in recovering coefficients of the pencil from the given Weyl-type function. The statement and the study of inverse spectral problems essentially depend on the structure of the closed set. We consider an important subclass of closed sets when the set is a unification of a finite number of closed intervals and isolated points.

Uniqueness of recovering arbitrary order differential operators on noncompact spatial networks

An inverse spectral problem is studied for arbitrary order differential operators on noncompact graphs. A uniqueness theorem of recovering potentials from the Weyl matrices is proved. 

On an inverse problem for differential operators on hedgehog-type graphs

An inverse spectral problem is studied for Sturm–Liouville differential operators on hedgehog-type graphs with generalized matching conditions in the interior vertices and with Dirichlet boundary conditions in the boundary vertices. A uniqueness theorem of recovering potentials from given spectral characteristics is provided, and a constructive solution for the inverse problem is obtained. 

Uniqueness of Solution of the Inverse Scattering Problem for Various Order Differential Equation on the Simplest Noncompact Graph with Cycle

An inverse scattering problem is studied for variable orders differential operators on simplest noncompact graph with cycle. A uniqueness theorem of recovering coefficients of operators from the scattering data is provided.

On Inverse Periodic Problem for Differential Operators for Central Symmetric Potentials

An inverse spectral problem for Sturm–Liouville operators on a finite interval with periodic boundary conditions is studied in the central symmetric case, when the potential is symmetric with respect to the middle of the interval. We discuss the statement of the problem, provide an algorithm for its solution along with necessary and sufficient conditions for the solvability of this nonlinear inverse problem.

On Recovering Differential Pencils on a Bush-type Graph

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.

Recovering Differential Operators on a Bush-Type Graph

An inverse spectral problem is studied for Sturm–Liouvilleoperators on arbitrary graphs with a cycle. A constructive procedure for the solution is provided and the uniquenness is established.

The Inverse Problem of Spectral Analysis for the Matrix Sturm – Liouville Equation

The inverse spectral problem is investigated for the matrix Sturm - Liouville equation on a finite interval. The article provides properties of spectral characteristics, a constructive procedure for the solution of the inverse problem along with necessary and sufficient conditions for its solvability has been obtained.

Uniqueness of the Solution of the Inverse Problem for Differential Operators on Arbitrary Compact Graphs

An inverse spectral problem is studied for Sturm – Liouville operators on arbitrary compact graphs with standard matching conditions in internal vertices. A uniqueness theorem of recovering operator’s coefficients from spectra is proved.

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