HALF INVERSE PROBLEM FOR THE IMPULSIVE DIFFUSION OPERATOR WITH DISCONTINUOUS COEFFICIENT

Abstract

The problem uniquely determination coefficients of operator by mixed spectral data consists in reconstruction on the interval by its spectrum and half of the potentials. In this paper, by using the Hocstadt-Lieberman and Yang-Zettl's methods we show that if p(x) and q(x) are known on the interval [π/2,π], then only one spectrum suffices to determine p(x) and q(x) on the interval [0,π] for impulsive diffusion operator with discontinuous coefficient.