一个带三点边条件的Sturm-Liouville问题的迹公式  

Some Traces for a Sturm-Liouville Problem with Three-point Boundary Conditions

作　　者：李灵晓[1] 张义宁[2] 

机构地区：[1]河南科技大学理学院,河南洛阳471003 [2]聊城大学数学系,山东聊城252059

出　　处：《河南科技大学学报（自然科学版）》2008年第1期74-77,共4页Journal of Henan University of Science And Technology:Natural Science

基　　金：河南省教育厅自然科学基金项目(2007110010);河南科技大学科研基金项目(2006ZY011,2006ZY001)

摘　　要：讨论了一个带三点边条件Sturm-Liouville问题的特征值的性质与渐近性质,并获得了折射情形下的各迹公式。按折射型的不同特殊情况将三点边条件分为3种基本类型,并得到相应的3个决定特征值的整函数ω(λ)及其相应围道上的渐近估计。采用留数方法,对该三点边条件Sturm-liouville问题的特征值进行估计,得到多种情况下的特征值的渐近迹公式。In this paper,some traces are obtained for a Sturm-Liouville problem with three-point boundary conditions by use of the residue method.According to its reflection type,this boundary conditions are categorized into three element types in different special cases,thus three corresponding entire functions deciding eigenvalue and their asymptotic estimations on the corresponding circuits are gotten.By restorting to the integral identity and the residue method,asymptotic estimations of the eigenvalue problem are considered and eigenvalue's trace identities are obtained.

关 键 词：三点边条件 特征值 渐近估计 ROUCHE定理 留数方法 迹公式 

分 类 号：O175.09[理学—数学]