Amirov R. Kh.
On impulsive Sturm - Liouville operators with singularity and spectral parameter in boundary conditions
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.
On impulsive Sturm–Liouville operators with Coulomb potential and spectral parameter linearly contained in boundary conditions
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.
Direct and inverse problems for the Dirac operator with a spectral parameter linearly contained in a boundary condition
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.
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.
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.