Half‐inverse problems for the quadratic pencil of the Sturm–Liouville equations with impulse

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 pointπ 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 given on0 π 2 . and (ii) the potentials given onπ 2 π , where 0 <  α  < 1 , respectively. Inverse spectral problems, Sturm–Liouville operator, spectrum, uniqueness.