scholarly journals An inverse spectral problem for differential operators with integral delay

2011 ◽  
Vol 42 (3) ◽  
pp. 295-303 ◽  
Author(s):  
Yulia Kuryshova
Keyword(s):  
Spectral Problem ◽  
Uniqueness Theorem ◽  
Liouville Operator ◽  
Differential Operators ◽  
Inverse Spectral Problem ◽  
Integral Transform ◽  
Main Tool ◽  
One Dimensional ◽  
Sturm Liouville ◽  
The Uniqueness Theorem

The uniqueness theorem is proved for the solution of the inverse spec- tral problem for second-order integro-di®erential operators on a ¯nite interval. These operators are perturbations of the Sturm-Liouville operator with convolution and one- dimensional operators. The main tool is an integral transform connected with solutions of integro-di®erential operators.

scholarly journals Inverse spectral problems for differential operators on a graph with a rooted cycle

2009 ◽  
Vol 40 (3) ◽  
pp. 271-286 ◽  
Author(s):  
V. Yurko
Keyword(s):  
Spectral Problem ◽  
Uniqueness Theorem ◽  
Differential Operators ◽  
Inverse Spectral Problem ◽  
Inverse Spectral Problems ◽  
Matching Conditions ◽  
Spectral Problems ◽  
Sturm Liouville ◽  
Inverse Spectral

An inverse spectral problem is studied for Sturm-Liouville differential operators on graphs with a cycle and with standard matching conditions in internal vertices. A uniqueness theorem is proved, and a constructive procedure for the solution is provided.

scholarly journals An inverse spectral problem for non-selfadjoint Sturm-Liouville operators with nonseparated boundary conditions

2012 ◽  
Vol 43 (2) ◽  
pp. 289-299 ◽  
Author(s):  
Vjacheslav Yurko
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Spectral Problem ◽  
Uniqueness Theorem ◽  
Inverse Spectral Problem ◽  
Finite Interval ◽  
Spectral Characteristics ◽  
Nonseparated Boundary Conditions ◽  
Sturm Liouville ◽  
Liouville Operators

Non-selfadjoint Sturm-Liouville operators on a finite interval with nonseparated boundary conditions are studied. We establish properties of the spectral characteristics and investigate an inverse problem of recovering the operators from their spectral data. For this inverse problem we prove a uniqueness theorem and provide a procedure for constructing the solution.

scholarly journals Sturm-Liouville differential operators with deviating argument

2017 ◽  
Vol 48 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Vjacheslav Anatoljevich Yurko ◽  
Sergey Alexandrovich Buterin ◽  
Milenko Pikula
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Differential Operators ◽  
Spectral Characteristics ◽  
Second Order ◽  
Constant Delay ◽  
Deviating Argument ◽  
Sturm Liouville ◽  
The Uniqueness Theorem

Non-selfadjoint second-order differential operators with a constant delay are studied. We establish properties of the spectral characteristics and investigate the inverse problem of recovering operators from their spectra. For this inverse problem the uniqueness theorem is proved.

scholarly journals An Inverse Spectral Problem for the Sturm-Liouville Operator on a Three-Star Graph

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
I. Dehghani Tazehkand ◽  
A. Jodayree Akbarfam
Keyword(s):  
Inverse Problem ◽  
Spectral Problem ◽  
Liouville Operator ◽  
Inverse Spectral Problem ◽  
Spectral Characteristics ◽  
Star Graph ◽  
Dirichlet Problems ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Robin Boundary

We study an inverse spectral problem for the Sturm-Liouville operator on a three-star graph with the Dirichlet and Robin boundary conditions in the boundary vertices and matching conditions in the internal vertex. As spectral characteristics,we consider the spectrum of the main problem together with the spectra of two Dirichlet-Dirichlet problems and one Robin-Dirichlet problem on the edges of the graph and investigate their properties and asymptotic behavior. We prove that if these four spectra do not intersect, then the inverse problem of recovering the operator is uniquely solvable.We give an algorithm for the solution of the inverse problem with respect to this quadruple of spectra.

scholarly journals Reconstruction of the Sturm-Liouville operators on a graph with $\delta'_s$ couplings

2011 ◽  
Vol 42 (3) ◽  
pp. 329-342 ◽  
Author(s):  
ChuanFu Yang
Keyword(s):  
Uniqueness Theorem ◽  
Liouville Operator ◽  
Dense Subset ◽  
Star Graph ◽  
Central Vertex ◽  
Inverse Nodal Problems ◽  
Sturm Liouville ◽  
The Given ◽  
The Uniqueness Theorem ◽  
Liouville Operators

Inverse nodal problems consist in constructing operators from the given zeros of their eigenfunctions. In this work, we deal with the inverse nodal problems of reconstructing the Sturm- Liouville operator on a star graph with $\delta'_s $ couplings at the central vertex. The uniqueness theorem is proved and a constructive procedure for the solution is provided from a dense subset of zeros of the eigenfunctions for the problem as a data.

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