INVERSE SPECTRAL PROBLEM FOR STURM-LIOUVILLE OPERATOR WITH BOTH JUMP CONDITIONS DEPENDENT ON THE SPECTRAL PARAMETER

The inverse spectral problem of Sturm-Liouville operator with both of the jump conditions dependent on the spectral parameter is investigated. Firstly, by theoretical operator formulation the self-adjointness of the problem is proven and then some of the eigenvalue properties, especially the asymptotic formulas of eigenvalues and eigenfunctions are given. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.