An analogue of Borg's uniqueness theorem in the case of indecomposable boundary conditions

Abstract

An uniqueness theorem for the inverse problem in the case of a second-order equation defined on the interval [0,1] when the boundary forms contain combinations of the values of functions at the points 0 and 1 is proved. The auxiliary eigenvalue problems in our theorem are chose in the same manner as in Borg's uniqueness theorem are not as in that of Sadovni\v ci$\check \imath $'s. So number of conditions in our theorem is less than that in Sadovni\v ci$\check\imath$'s.