Half-inverse problems for the quadratic pencil of theSturm-Liouvilleequations with impulse

Abstract

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 urn:x-wiley:0749159X:media:num22559:num22559-math-0001. 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 on urn:x-wiley:0749159X:media:num22559:num22559-math-0002 and (ii) the potentials given on urn:x-wiley:0749159X:media:num22559:num22559-math-0003, where 0 < α < 1, respectively.