Inverse Spectral Problems for Linear Differential Operators and Their Applications

2000 ◽  
Author(s):  
V A Yurko
Keyword(s):  
Differential Operators ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Linear Differential Operators ◽  
Inverse Spectral ◽  
Linear Differential

Inverse spectral problems for differential operators with non-separated boundary conditions

2020 ◽  
Vol 28 (4) ◽  
pp. 567-616
Author(s):  
Vjacheslav A. Yurko
Keyword(s):  
Inverse Problems ◽  
Boundary Conditions ◽  
Differential Operators ◽  
Spectral Characteristics ◽  
Short Review ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Separated Boundary Conditions ◽  
Inverse Spectral ◽  
Type Boundary

AbstractWe give a short review of results on inverse spectral problems for second-order differential operators on an interval with non-separated boundary conditions. We pay the main attention to the most important nonlinear inverse problems of recovering coefficients of differential operators from given spectral characteristics. In the first part of the review, we provide the main results and methods related to inverse problems for Sturm–Liouville operators with non-separated boundary conditions: periodic, quasi-periodic and Robin-type boundary conditions. At the end, we present the main results on inverse problems for differential pencils with non-separated boundary conditions.

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.

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