Inverse spectral problems for Sturm-Liouville operators with partial information

In this paper, we study the inverse spectral problems for Sturm-Liouville operators with Robin boundary conditions and show that if the potential q on the interval [0,α] for some α∈[0,1) is given a priori, then the potential q on the whole interval [0,1] can be uniquely determined by a subset of pairs of eigenvalues and the weight numbers of the corresponding eigenvalues or by parts of two spectra.