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

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.

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