确定Sturm-Liouville问题中系数的反问题

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

中文关键词:  Sturm-Liouville问题  反问题

英文关键词:Sturm-Liouville problem  inverse problem

中文摘要:

      讨论确定Sturm－Liouville问题中算子的系数α（x）或者q（x）的问题．在一定条件下，系数α（x）或者q（x）可由数据或者数据唯一确定，这里的u_j（x）满足而构成L²（0，1）的一个基，α和β为给定的实数.

英文摘要:

      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).