Inverse Sturm-Liouville problems with a Spectral Parameter in the Boundary and transmission conditions

In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator −D2+q with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining a new Hilbert space and using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at some interior point and parts of two sets of eigenvalues.