Spectral problems for Sturm–Liouville operator with boundary and jump conditions linearly dependent on the eigenparameter

In this study, a boundary-value problem is considered, which is generated by Sturm-Liouville differential equation, parameter-dependent boundary conditions and discontinuity (or jump) conditions. The properties of the eigenvalues of this problem are investigated. Uniqueness theorems for the solution of inverse problem according to the Weyl function and spectral data are proven

Inverse Sturm–Liouville problems with eigenvalue-dependent boundary and discontinuity conditions

An impulsive boundary-value problem generated by Sturm-Liouville differential equation with the eigenvalue parameter non-linearly contained in one boundary condition and in the jump conditions is considered. It is shown that the coefficients of the problem is uniquely determined either by the Weyl function or by Prufer's angle. It is also proven that two given spectra uniquely determine the coefficients of the problem