scholarly journals Half Inverse Problem for the Sturm-Liouville Operator with Coulomb potential

2014 ◽  
Vol 8 (2) ◽  
pp. 501-504 ◽  
Author(s):  
Murat Sat
Keyword(s):  
Inverse Problem ◽  
Coulomb Potential ◽  
Liouville Operator ◽  
Half Inverse Problem ◽  
Sturm Liouville

On the Hochstadt–Lieberman type problem with eigenparameter dependent boundary condition

2020 ◽  
Vol 28 (4) ◽  
pp. 557-565
Author(s):  
Sheng-Yu Guan ◽  
Chuan-Fu Yang ◽  
Natalia Bondarenko ◽  
Xiao-Chuan Xu ◽  
Yi-Teng Hu
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Existence Theorem ◽  
Liouville Operator ◽  
Entire Functions ◽  
Finite Interval ◽  
Type Problem ◽  
Reconstruction Procedure ◽  
Half Inverse Problem ◽  
Sturm Liouville

AbstractThe half-inverse problem is studied for the Sturm–Liouville operator with an eigenparameter dependent boundary condition on a finite interval. We develop a reconstruction procedure and prove the existence theorem for solution of the inverse problem. Our method is based on interpolation of entire functions.

scholarly journals Direct and Inverse Problems for Sturm-Liouville Operator Which Has Discontinuity Conditions and Coulomb Potential

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yalçın Güldü ◽  
Merve Arslantaş
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Unique Solvability ◽  
Coulomb Potential ◽  
Liouville Operator ◽  
Direct And Inverse Problems ◽  
Main Equation ◽  
Sturm Liouville ◽  
Discontinuity Conditions

We give a derivation of the main equation for Sturm-Liouville operator with Coulomb potential and prove its unique solvability. Using the solution of the main equation, we get an algorithm for the solution of the inverse problem.

scholarly journals An inverse problem for the non-self-adjoint matrix Sturm-Liouville operator

2018 ◽  
Vol 50 (1) ◽  
pp. 71-102 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problem ◽  
Liouville Operator ◽  
Finite Interval ◽  
Spectral Characteristics ◽  
Sufficient Conditions ◽  
Adjoint Matrix ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville ◽  
Necessary And Sufficient

The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary and sufficient conditions for the solvability of the inverse problem. Our approach is based on the constructive solution of the inverse problem by the method of spectral mappings. The characterization of the spectral data in the self-adjoint case is given as a corollary of the main result.

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