Uniqueness of the Solution to the Inverse Problem of Scattering Theory for the Sturm--Liouville Operator with a Spectral Parameter in the Boundary Condition

2003 ◽  
Vol 74 (1/2) ◽  
pp. 136-140 ◽  
Author(s):  
Kh. R. Mamedov
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Spectral Parameter ◽  
Liouville Operator ◽  
Scattering Theory ◽  
Uniqueness Of The Solution ◽  
Sturm Liouville

scholarly journals An inverse problem for the second-order integro-differential pencil

2019 ◽  
Vol 50 (3) ◽  
pp. 223-231 ◽  
Author(s):  
Natalia P. Bondarenko
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Spectral Parameter ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Uniqueness Of Solution ◽  
Convolution Kernel ◽  
Sturm Liouville ◽  
Necessary And Sufficient

We consider the second-order (Sturm-Liouville) integro-differential pencil with polynomial dependence on the spectral parameter in a boundary condition. The inverse problem is solved, which consists in reconstruction of the convolution kernel and one of the polynomials in the boundary condition by using the eigenvalues and the two other polynomials. We prove uniqueness of solution, develop a constructive algorithm for solving the inverse problem, and obtain necessary and sufficient conditions for its solvability.

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.

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.

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