Browsing by Author "Khalili, Yasser"

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Citation - WoS: 0
Citation - Scopus: 0
The Inverse Problem for the Impulsive Differential Pencil
(Maik Nauka/interperiodica/springer, 2024) Baleanu, Dumitru; Baleanu, Dumitru; Matematik
In this paper, we investigate the inverse problem for the impulsive differential pencil in the finite interval. Taking Mochizuki-Trooshin's theorem, it is proved that two potentials and the boundary conditions are uniquely given by one spectra together with a set of values of eigenfunctions in the situation of x = 1/2. Moreover, applying Gesztesy-Simon's theorem, we demonstrate that if the potentials are assumed on the interval [(1-theta)/2, 1], where theta is an element of (0, 1), a finite number of spectrum are enough to give potentials on [0, 1] and other boundary condition.
Citation - WoS: 2
Citation - Scopus: 2
Inverse problems for the impulsive Sturm-Liouville operator with jump conditions
(Taylor & Francis Ltd, 2019) Khalili, Yasser; Baleanu, Dumitru; Kadkhoda, Nematollah; Baleanu, Dumitru; 56389; Matematik
The inverse problem for impulsive Sturm-Liouville operators with discontinuity conditions is considered. We have shown that all parameters used in the boundary conditions as well as can be uniquely established by a set of values of eigenfunctions at the mid-point and one spectrum. Moreover, we discuss Gesztesy-Simon theorem and show that if the potential function is prescribed on the interval for some , then parts of a finite number of spectra suffice to determine on .
Citation - WoS: 5
Citation - Scopus: 5
On the determination of the impulsive Sturm-Liouville operator with the eigenparameter-dependent boundary conditions
(Wiley, 2020) Khalili, Yasser; Baleanu, Dumitru; Kadkhoda, Nematollah; Baleanu, Dumitru; 56389; Matematik
In the present work, we consider the inverse problem for the impulsive Sturm-Liouville equations with eigenparameter-dependent boundary conditions on the whole interval (0,pi) from interior spectral data. We prove two uniqueness theorems on the potential q(x) and boundary conditions for the interior inverse problem, and using the Weyl function technique, we show that if coefficients of the first boundary condition, that is, h(1),h(2), are known, then the potential function q(x) and coefficients of the second boundary condition, that is, H-1,H-2, are uniquely determined by information about the eigenfunctions at the midpoint of the interval and one spectrum or partial information on the eigenfunctions at some internal points and some of two spectra.
Citation - WoS: 5
Citation - Scopus: 5
Recovering differential pencils with spectral boundary conditions and spectral jump conditions
(Springer, 2020) Khalili, Yasser; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
In this work, we discuss the inverse problem for second order differential pencils with boundary and jump conditions dependent on the spectral parameter. We establish the following uniqueness theorems: (i) the potentials q(k)(x) and boundary conditions of such a problem can be uniquely established by some information on eigenfunctions at some internal point b is an element of (pi/2, pi) and parts of two spectra; (ii) if one boundary condition and the potentials qk(x) are prescribed on the interval [pi/2(1 - alpha), pi] for some alpha is an element of (0, 1), then parts of spectra S subset of sigma(L) are enough to determine the potentials q(k)(x) on the whole interval [0, pi] and another boundary condition.