Inverse problems for Sturm-Liouville equations with boundary conditions polynomially dependent on the spectral parameter

Sturm-Liouville differential operators in a finite interval with boundary conditions depending polynomially on the spectral parameter are studied. We establish the properties of the spectral characteristics and investigate three inverse problems of recovering the operator either from the so-called Weyl function, or from discrete spectral data or from two spectra. For these inverse problems we provide procedures for constructing their solutions by the method of spectral mappings.