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 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.

scholarly journals A unuqueness theorem for Sturm-Lioville operators with eigenparameter dependent boundary conditions

2012 ◽  
Vol 43 (1) ◽  
pp. 145-152 ◽  
Author(s):  
Yu-Ping Wang
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Boundary Conditions ◽  
Uniqueness Theorem ◽  
Linear Function ◽  
Spectral Parameter ◽  
Finite Interval ◽  
Sturm Liouville ◽  
Fractional Linear Function ◽  
Liouville Operators

In this paper, we discuss the inverse problem for Sturm- Liouville operators with boundary conditions having fractional linear function of spectral parameter on the finite interval $[0, 1].$ Using Weyl m-function techniques, we establish a uniqueness theorem. i.e., If q(x) is prescribed on $[0,\frac{1}{2}+\alpha]$ for some $\alpha\in [0,1),$ then the potential $q(x)$ on the interval $[0, 1]$ and fractional linear function $\frac{a_2\lambda+b_2}{c_2\lambda+d_2}$  of the boundary condition are uniquely determined by a subset $S\subset \sigma (L)$ and fractional linear function $\frac{a_1\lambda+b_1}{c_1\lambda+d_1}$ of the boundary condition.

scholarly journals Inverse Sturm-Liouville problem with analytical functions in the boundary condition

2020 ◽  
Vol 18 (1) ◽  
pp. 512-528 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problem ◽  
Entire Functions ◽  
Sufficient Conditions ◽  
Liouville Problem ◽  
Local Solvability ◽  
Cauchy Data ◽  
Problem Solution ◽  
Analytical Functions ◽  
Half Inverse Problem ◽  
Sturm Liouville

Abstract The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness and develop a constructive algorithm for the inverse problem solution. The main results are applied to the Hochstadt-Lieberman half-inverse problem. As an auxiliary proposition, we prove local solvability and stability for the inverse Sturm-Liouville problem by the Cauchy data in the non-self-adjoint case.

scholarly journals An inverse problem for the Sturm-Liouville pencil with arbitrary entire functions in the boundary condition

2020 ◽  
Vol 14 (1) ◽  
pp. 153-169 ◽  
Author(s):  
Chuan-Fu Yang ◽  
◽  
Natalia Pavlovna Bondarenko ◽  
Xiao-Chuan Xu ◽  
◽  
...  
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Entire Functions ◽  
Sturm Liouville
Sign in / Sign up

Export Citation Format

Share Document