边界条件都含有特征参数的四阶微分算子特征值的依赖性  

Dependence of Eigenvalues of Fourth-order Differential Operator with Eigenparameters Contained in the All Boundary Conditions

作　　者：许美珍[1] 闫文文 纪安桐 XU MEIZHEN;YAN WENWEN;JI ANTONG(College of Sciences,Inner Mongolia University of Technology,Hohhot 010051,China)

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051

出　　处：《应用数学学报》2023年第5期705-720,共16页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:11561051);内蒙古自然科学基金(批准号:2021MS01020,2023IHMS01015)资助项目。

摘　　要：本文考虑了区间[a,b]两端四个边界条件都含有特征函数的四阶微分算子特征值的依赖性问题,证明了特征值不仅连续依赖而且可微依赖于问题的各个参数(系数函数,权函数,区间端点,边界条件系数矩阵),并且给出了相应的微分表达式.特别地,给出特征值关于特征参数依赖的边界条件系数矩阵的Frechet导数.This paper considers the dependence of eigenvalues of fourth-order differential operator with eigenparameters in the four boundary conditions of both ends of the interval[a,b].It is proved that the eigenvalues depend not only continuously but also smoothly on the parameters of the problem(the coefficient functions,the weight function,the interval endpoints,boundary conditions coefficient matrix),and give the corresponding differential expressions.In particular,the Frechet derivative of the eigenvalue with respect to the eigenparameter-dependent boundary conditions coefficient matrix is given.

关 键 词：四阶微分算子 特征参数 特征值的依赖性 可微性 Frechet导数 

分 类 号：O175.3[理学—数学]