The interior inverse problem for the impulsive Sturm-Liouville equation

In the present paper, inverse problems are considered for the impulsive SturmLiouville equations in the finite interval. We use formulations of the inverse problem the so called Mochizuki-Trooshin theorem and demonstrate that the coefficients of the considered problem are uniquely determined by values of the eigenfunctions in the middle of the interval and one spectrum. We also prove that some information on eigenfunctions at some internal point b is an element of (1/2, 1) and parts of two spectra suffice to determine all coefficients in the boundary value problem.