Half Inverse Problem for the Impulsive Diffusion Operator with Discontinuous Coefficient

Abstract

The half inverse problem is to construct coefficients of the operator in a whole interval by using one spectrum and potential known in a semi interval. 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 (pi/2; pi), then only one spectrum suffices to determine p (x); q( x) functions and beta, h coefficients on the interval (0; pi) for impulsive diffusion operator with discontinuous coefficient.