An inverse problem for the non-selfadjoint matrix Sturm–Liouville equation on the half-line

2007 ◽  
Vol 15 (8) ◽  
Author(s):  
G. Freiling ◽  
V. Yurko
Keyword(s):  
Inverse Problem ◽  
Liouville Equation ◽  
Half Line ◽  
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.

An inverse problem for Sturm–Liouville operators on the half-line with complex weights

2019 ◽  
Vol 27 (3) ◽  
pp. 439-443
Author(s):  
Vjacheslav Yurko
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Operators ◽  
Spectral Characteristics ◽  
Half Line ◽  
Sturm Liouville ◽  
The Given ◽  
Complex Valued ◽  
The Uniqueness Theorem ◽  
Liouville Operators

Abstract Second order differential operators on the half-line with complex-valued weights are considered. Properties of spectral characteristics are established, and the inverse problem of recovering operator’s coefficients from the given Weyl-type function is studied. The uniqueness theorem is proved for this class of nonlinear inverse problems, and a number of examples are provided.

scholarly journals An inverse problem for Sturm-Liouville operators on the half-line having Bessel-type singularity in an interior point

2013 ◽  
Vol 11 (12) ◽  
Author(s):  
Alexey Fedoseev
Keyword(s):  
Inverse Problem ◽  
Interior Point ◽  
Sufficient Conditions ◽  
Weyl Function ◽  
Half Line ◽  
Type Singularity ◽  
Sturm Liouville ◽  
Necessary And Sufficient ◽  
The Given ◽  
Liouville Operators

AbstractWe study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided, also necessary and sufficient conditions for the solvability of the inverse problem are obtained.

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