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.

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 Inverse nodal problem for p−Laplacian Bessel equation with polynomially dependent spectral parameter

2018 ◽  
Vol 51 (1) ◽  
pp. 255-263
Author(s):  
Emrah Yilmaz ◽  
Mudhafar Hamadamen ◽  
Tuba Gulsen
Keyword(s):  
Boundary Condition ◽  
Liouville Equation ◽  
Reconstruction Formula ◽  
Bessel Equation ◽  
Inverse Nodal Problem ◽  
Laplacian Energy ◽  
Sturm Liouville ◽  
Nodal Problem ◽  
Energy Dependent ◽  
Prüfer Substitution

Abstract In this study, solution of inverse nodal problem for p−Laplacian Bessel equation is extended to the case that boundary condition depends on polynomial eigenparameter. To find spectral datas as eigenvalues and nodal parameters of this problem, we used a modified Prüfer substitution. Then, reconstruction formula of the potential functions is also obtained by using nodal lenghts. However, this method is similar to used in [Koyunbakan H., Inverse nodal problem for p−Laplacian energy-dependent Sturm-Liouville equation, Bound. Value Probl., 2013, 2013:272, 1-8], our results are more general.

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