The Inverse Problem for the Impulsive Differential Pencil

Abstract

In this paper, we investigate the inverse problem for the impulsive differential pencil in the finite interval. Taking Mochizuki-Trooshin's theorem, it is proved that two potentials and the boundary conditions are uniquely given by one spectra together with a set of values of eigenfunctions in the situation of x = 1/2. Moreover, applying Gesztesy-Simon's theorem, we demonstrate that if the potentials are assumed on the interval [(1-theta)/2, 1], where theta is an element of (0, 1), a finite number of spectrum are enough to give potentials on [0, 1] and other boundary condition.