scholarly journals A Half-Inverse Problem for Impulsive Dirac Operator with Discontinuous Coefficient

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Yalçın Güldü
Keyword(s):  
Inverse Problem ◽  
Dirac Operator ◽  
Potential Function ◽  
Differential Operators ◽  
Discontinuous Coefficient ◽  
Single Spectrum ◽  
Half Inverse Problem ◽  
Discontinuity Conditions

An inverse problem for Dirac differential operators with discontinuity conditions and discontinuous coefficient is studied. It is shown by Hochstadt and Lieberman's method that if the potential function in is prescribed over the interval , then a single spectrum suffices to determine on the interval and it is also shown here that is uniquely determined by a spectrum.

scholarly journals An interior inverse problem for the impulsive Dirac operator

2011 ◽  
Vol 42 (3) ◽  
pp. 259-263 ◽  
Author(s):  
Sinan Özkan ◽  
Rauf Kh. Amirov
Keyword(s):  
Inverse Problem ◽  
Dirac Operator ◽  
Potential Function ◽  
Differential Operators ◽  
Internal Point

In this study, an inverse problem for Dirac differential operators with discontinuities is studied. It is shown that the potential function can be uniquely determined by a set of values of eigenfunctions at some internal point and one spectrum.

scholarly journals Half inverse problem for the impulsive diffusion operator with discontinuous coefficient

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 157-168 ◽  
Author(s):  
Yaşar Çakmak ◽  
Seval Işık
Keyword(s):  
Inverse Problem ◽  
Discontinuous Coefficient ◽  
Diffusion Operator ◽  
Impulsive Diffusion ◽  
Half Inverse Problem

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.

Half-inverse problem for the Dirac operator

2019 ◽  
Vol 87 ◽  
pp. 172-178 ◽  
Author(s):  
Chuan-Fu Yang ◽  
Dai-Quan Liu
Keyword(s):  
Inverse Problem ◽  
Dirac Operator ◽  
Half Inverse Problem

scholarly journals Recovering singular differential operators on noncompact star-type graphs from Weyl functions

2011 ◽  
Vol 42 (2) ◽  
pp. 223-236
Author(s):  
V. Yurko
Keyword(s):  
Inverse Problem ◽  
Uniqueness Theorem ◽  
Differential Operators ◽  
Spectral Characteristics ◽  
Method Of Spectral Mappings ◽  
Weyl Functions

Bessel-type differential operators on noncompact star-type graphs are studied. We establish properties of the spectral characteristics and then we investigate the inverse problem of recovering the operator from the so-called Weyl vector. For this inverse problem we prove a uniqueness theorem and propose a procedure for constructing the solution using the method of spectral mappings.

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.

Inverse nodal problems for integro-differential operators with a constant delay

2019 ◽  
Vol 27 (4) ◽  
pp. 501-509 ◽  
Author(s):  
Murat Sat ◽  
Chung Tsun Shieh
Keyword(s):  
Integral Operator ◽  
Potential Function ◽  
Liouville Operator ◽  
Differential Operators ◽  
Constant Delay ◽  
Nodal Points ◽  
Inverse Nodal Problems ◽  
Volterra Integral Operator ◽  
Sturm Liouville

Abstract We study inverse nodal problems for Sturm–Liouville operator perturbed by a Volterra integral operator with a constant delay. We have estimated nodal points and nodal lengths for this operator. Moreover, by using these data, we have shown that the potential function of this operator can be established uniquely.

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