Green’s Functions of a Class of Sturm-Liouville Problems with Eigenparameters in Boundary Conditions  

一类边界条件含有特征参数的Sturm-Liouville问题的格林函数

作　　者：XIAO Lu MU Dan ZHANG Ruifan 肖露;牡丹;张瑞凡(湖北民族大学数学与统计学院,恩施445000)

机构地区：[1]School of Mathematics and Statistics,Hubei University for Nationalities,Enshi 445000,China

出　　处：《数学理论与应用》2025年第1期94-106,共13页Mathematical Theory and Applications

基　　金：supported by the National Natural Science Foundation of China(No.12461086);the Natural Science Foundation of Hubei Province(No.2022CFC016)。

摘　　要：In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem.本文研究一类边界条件含有特征参数的Sturm-Liouville问题.首先定义一个依赖于转移条件的新内积,得到一个新的Hilbert空间,在新的Hilbert空间中研究的算子A是自共轭的.然后构造与问题相关的基本解,得到特征值的充要条件,并证明特征值是简单的.最后我们对这类问题的格林函数进行讨论.

关 键 词：Sturm-Liouville problem Eigenparameter-dependent boundary condition Green’s function 

分 类 号：O175.2[理学—数学]