Half inverse problems for the impulsive quadratic pencil with the discontinouty coefficient

Abstract

In this paper, we study the inverse spectral problem for the quadratic differential pencils with discontinouty coefficient on [0, π] with seperably boundary conditions and the impulsive conditions at the point x = π 2 . We prove that two potentials functions on the interval [0, π] and the parameters in the boundary and impulsive conditions can be determined from a sequence of eigenvalues for two cases: (i) The potentials is given onThe potentials is given on ( π) , where 0 < α < 1 , respectively.