half inverse problem
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2020 ◽  
Vol 28 (6) ◽  
pp. 775-782
Author(s):  
İbrahi̇m Adalar ◽  
Ahmet Sinan Ozkan

AbstractIn this paper, a Sturm–Liouville boundary value problem which includes conformable fractional derivatives of order α, {0<\alpha\leq 1} is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra and classical spectral data. We also study the half-inverse problem and prove a Hochstadt–Lieberman-type theorem.


2020 ◽  
Vol 28 (4) ◽  
pp. 557-565
Author(s):  
Sheng-Yu Guan ◽  
Chuan-Fu Yang ◽  
Natalia Bondarenko ◽  
Xiao-Chuan Xu ◽  
Yi-Teng Hu

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.


2020 ◽  
Vol 18 (1) ◽  
pp. 512-528 ◽  
Author(s):  
Natalia Pavlovna Bondarenko

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.


2019 ◽  
Vol 87 ◽  
pp. 172-178 ◽  
Author(s):  
Chuan-Fu Yang ◽  
Dai-Quan Liu

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 157-168 ◽  
Author(s):  
Yaşar Çakmak ◽  
Seval Işık

The half inverse problem is to construct coefficients of the operator in a whole interval by using one spectrum and potential known in a semi interval. In this paper, by using the Hocstadt-Lieberman and Yang-Zettl?s methods we show that if p(x) and q(x) are known on the interval (?/2,?), then only one spectrum suffices to determine p (x),q(x) functions and ?,h coefficients on the interval (0,?) for impulsive diffusion operator with discontinuous coefficient.


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