Determination of differential pencils with impulse from interior spectral data

In this paper, we are concerned with the inverse spectral problems for differential pencils defined on [ 0 , π ] with an interior discontinuity. We prove that two potential functions are determined uniquely by one spectrum and a set of values of eigenfunctions at some interior point b ∈ ( 0 , π ) in the situation of b = π / 2 and b ≠ π / 2 . For the latter, we need the knowledge of a part of the second spectrum.