half inverse problems for the singular sturm-liouville operator

In this paper, we consider the inverse spectral problem for the impulsive sturm-liouville differential pencils on [0, π] with the robin boundary conditions and the jump conditions at the point π/2. we prove that two potentials functions on the whole interval and the parameters in the boundary and jump conditions can be determined from a set of eigenvalues for two cases: (i) the potentials are given on (0, π/4 (α + β)). (ii) the potentials is given on (π/4 ( α + β), π/2 (α + β)), where 0 < α < β < 1 and α + β > 1, respectively.