An Inverse Problem of Determining the Coefficients in a Sturm-Liouville Problem

Abstract:

      We discuss the problem of determining the coefficients a (x) or q (x) of the operator in a Sturm-Liouville system. Under certain conditions, the coefficients a (x) or q (x) can be uniquely determined by the data Where u_j(x) solves Lu_j(x) =ψ_j(x),x∈(0, 1),u_j(0)cosα+u_j′(0)sinα=0, u_j(1)cosβ+u′_j(1)sinβ=0,and is a basis of L²(0, 1).