边界条件含谱参数的S-L算子反问题  

Inverse Problems for Sturm-Liouville Operators with One Boundary Condition Having the Spectral Parameter

作　　者：唐勇 王於平[2] Yong TANG;Yu Ping WANG(Information and Computational Sciences,College of Science,Nanjing Forestry University,Nanjing 210037,P.R.China;Department of Applied Mathematics,Nanjing Forestry University,Nanjing 210037,P.R.China)

机构地区：[1]南京林业大学理学院,南京210037 [2]南京林业大学应用数学系,南京210037

出　　处：《数学学报（中文版）》2023年第5期881-888,共8页Acta Mathematica Sinica：Chinese Series

基　　金：江苏省大学生创新项目(202110298138H)。

摘　　要：本文用混合谱数据研究边界条件含谱参数的Sturm-Liouville算子反问题.已知[a0,1]上的势函数q(x),我们证明一组谱的部分特征值唯一确定[0,1]上的势函数q(x).此外,还证明了缺少两个特征值的一组谱也能唯一确定[0,1]上的势函数q(x).The inverse spectral problems for Sturm-Liouville operators with one boundary condition having the spectral parameter are studied from mixed spectral data in this paper.The authors show that if the potential q(α)on[ao,1]is given a priori,then the potential q(a)on[0,1]can be uniquely determined by parts of one spectrum.In addition,we prove that the potential q(a)on[0,1]can be uniquely determined by one spectrum with two eigenvalues missing.

关 键 词：反问题 S-L算子 参数边界条件 混合谱数据 缺少特征值问题 

分 类 号：O175.3[理学—数学]