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.