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.