边界条件含有谱参数的奇异Sturm-Liouville算子特征值的依赖性  

Dependence of eigenvalue of Sturm-Liouville problem with singular potential and eigenparameter-dependent boundary conditions

作　　者：仲林路 杜高峰 ZHONG Linlu;DU Gaofeng(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《浙江大学学报(理学版)》2025年第3期391-396,共6页Journal of Zhejiang University(Science Edition)

基　　金：国家自然科学基金资助项目(12461039)。

摘　　要：研究了一类具有分布势函数的Sturm-Liouville算子特征值的依赖性。通过建立边界条件空间,构造嵌入映射,证明了特征值分支的连续依赖性,并且在Fréchet导数意义下,获得了特征值分支关于所有参数的微分表达式。In this paper,we study the dependence of eigenvalue of Sturm-Liouville operator with distributed potential function and prove the continuous dependence of eigenvalue branch by establishing boundary condition space and constructing embedded mapping.Moreover,in the sense of Fréchet derivative,the differential expressions of eigenvalue branches with respect to all given parameters are obtained.

关 键 词：奇异Sturm-Liouville算子 特征参数 特征值分支 连续依赖性 

分 类 号：O175.8[理学—数学]