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 discontinuity coefficient on [0, π] with separable boundary conditions and the impulsive conditions at the point x = π 2 . We prove that two potential 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 are given on ( 0, π 4 (1 + α) ) , (ii) The potentials are given on (π 4 (1 + α) , π ) , where 0 < α < 1, respectively.