2019
Том 71
№ 10

All Issues

Amirov R. Kh.

Articles: 5
Article (English)

On impulsive Sturm - Liouville operators with singularity and spectral parameter in boundary conditions

Amirov R. Kh., Güldü Y., Topsakal N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 12. - pp. 1610-1629

We study properties and the asymptotic behavior of spectral characteristics for a class of singular Sturm-Liouville differential operators with discontinuity conditions and an eigenparameter in boundary conditions. We also determine the Weyl function for this problem and prove uniqueness theorems for a solution of the inverse problem corresponding to this function and spectral data.

Article (English)

On impulsive Sturm–Liouville operators with Coulomb potential and spectral parameter linearly contained in boundary conditions

Amirov R. Kh., Güldü Y., Topsakal N.

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Ukr. Mat. Zh. - 2010. - 62, № 9. - pp. 1155–1172

The Sturm–Liouville problem with linear discontinuities is investigated in the case where an eigenparameter appears not only in a differential equation but also in boundary conditions. Properties and the asymptotic behavior of spectral characteristics are studied for the Sturm–Liouville operators with Coulomb potential that have discontinuity conditions inside a finite interval. Moreover, the Weyl function for this problem is defined and uniqueness theorems are proved for a solution of the inverse problem with respect to this function.

Article (English)

Direct and inverse problems for the Dirac operator with a spectral parameter linearly contained in a boundary condition

Amirov R. Kh., Keskin B., Özkan G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 9. - pp. 1155-1166

We investigate a problem for the Dirac differential operators in the case where an eigenparameter not only appears in the differential equation but is also linearly contained in a boundary condition. We prove uniqueness theorems for the inverse spectral problem with known collection of eigenvalues and normalizing constants or two spectra.

Article (Russian)

On a System of Dirac Differential Equations with Discontinuity Conditions Inside an Interval

Amirov R. Kh.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 5. - pp. 601–613

We study representations of solutions of the Dirac equation, properties of spectral data, and inverse problems for the Dirac operator on a finite interval with discontinuity conditions inside the interval.

Article (Russian)

On differential operators with singularity and conditions of discontinuity inside an interval

Amirov R. Kh., Yurko V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 11. - pp. 1443-1457

We investigate boundary-value problems for differential equations with singularity and discontinuity conditions inside an interval. We describe properties of the spectrum, prove a theorem on the completeness of eigenfunctions and associated functions, and study the inverse spectral problem.