scholarly journals Inverse problem for the Sturm–Liouville equation with piecewise entire potential and piecewise constant weight on a curve

2021 ◽  
Vol 18 (2) ◽  
pp. 951-974
Author(s):  
A. A. Golubkov
Keyword(s):  
Inverse Problem ◽  
Liouville Equation ◽  
Constant Weight ◽  
Piecewise Constant ◽  
Sturm Liouville

scholarly journals Inverse problem for Sturm-Liouville operators on a curve

2019 ◽  
Vol 50 (3) ◽  
pp. 349-359
Author(s):  
Andrey Aleksandrovich Golubkov ◽  
Yulia Vladimirovna Kuryshova
Keyword(s):  
Inverse Problem ◽  
Asymptotic Behavior ◽  
Transfer Matrix ◽  
Liouville Equation ◽  
Inverse Spectral Problem ◽  
Rectifiable Curve ◽  
Uniqueness Of The Solution ◽  
Sturm Liouville ◽  
Discontinuity Conditions ◽  
Liouville Operators

he inverse spectral problem for the Sturm-Liouville equation with a piecewise-entire potential function and the discontinuity conditions for solutions on a rectifiable curve \(\gamma \subset \textbf{C}\) by the transfer matrix along this curve is studied. By the method of a unit transfer matrix the uniqueness of the solution to this problem is proved with the help of studying of the asymptotic behavior of the solutions to the Sturm-Liouville equation for large values of the spectral parameter module.

scholarly journals Spectral analysis for the matrix Sturm-Liouville operator on a finite interval

2011 ◽  
Vol 42 (3) ◽  
pp. 305-327 ◽  
Author(s):  
Natalia Bondarenko
Keyword(s):  
Inverse Problem ◽  
Spectral Analysis ◽  
Liouville Equation ◽  
Inverse Spectral Problem ◽  
Finite Interval ◽  
Spectral Characteristics ◽  
Sufficient Conditions ◽  
The Matrix ◽  
Sturm Liouville ◽  
Necessary And Sufficient

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

scholarly journals Reconstruction of energy-dependent Sturm-Liouville equations from two spectra. II

2013 ◽  
Vol 5 (2) ◽  
pp. 315-325
Author(s):  
N.I. Pronska
Keyword(s):  
Inverse Problem ◽  
Liouville Equation ◽  
New Method ◽  
Sturm Liouville ◽  
Energy Dependent

We study the problem of reconstruction of singular energy-dependent Sturm-Liouville equation from two spectra. We suggest a new method of solving this inverse problem by establishing its connection with the problem of reconstruction from one spectrum and the set of norming constants.

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