A uniqueness theorem for the boundary value problems with non-linear dependence on the spectral parameter in the boundary conditions

An inverse spectral problem is considered for the non-self-adjoint Sturm-Liouville differential equation on a finite interval with boundary conditions depending polynomially on the spectral parameter. We give a formulation of an associated inverse problem and prove a corresponding uniqueness theorem. The obtained result is a generalization of the similar result for the classical Sturm-Liouville operator on a finite interval.