Direct and Inverse Problem for the Sturm--Liouville Operator with Eigenparameter-Dependent Boundary Conditions with Two Interior Discontinuities

In this paper, we study the Sturm-Liouville operator with two interior discontinuities and with spectral parameter linearly contained in one of the boundary conditions. Spectral properties of the eigenvalues and norming constants of this operator are investigated. Moreover, the Weyl solution and the Weyl function for this operator are defined. We prove uniqueness theorems for the solution of the inverse problem of reconstruction of the operator from the Weyl function, from the spectral data and from two spectra.