摘要
在有限区间上研究了带有分离型边值条件的Sturm-Liouville逆结点问题.通过对特征函数结点的分布情况和系统特征值的渐近性进行分析,给出了密度函数或势函数由特征函数结点能唯一确定的条件.证明了当势函数确定时,密度函数可以被特征函数结点的稠密子集基于常数倍意义下唯一确定;当密度函数已知时,势函数可由系统中相同的结点唯一确定.
The inverse Sturm-Liouville problem on a finite interval with separated boundary-value conditions is considered.Through analysing the asymptoticity of eigenvalues and the nodes of eigenfunction, give conditions that density function and potential function can be uniquely determined by the nodes.It is proved that density function can be uniquely determined up to a multiplicative constant by a dense subset of nodal positions when the potential function is given;and the potential function can be uniquely determined by the same nodal positions of systems when the density function is given.
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2011年第5期20-22,108,共4页
Journal of Shaanxi Normal University：Natural Science Edition
基金
国家自然科学基金资助项目(10771165)
