Sturm-Liouville问题的特征值  

Eigenvalue problems for a class of Sturm-Liouville problems with eigenparameters for both boundary conditions and transmission conditions

作　　者：张瑞凡 牡丹 ZHANG Ruifan;MU Dan(School of Mathematics and Statistics,Hubei University for Nationalities,En'shi 445000,China)

机构地区：[1]湖北民族大学数学与统计学院,湖北恩施445000

出　　处：《纯粹数学与应用数学》2025年第1期179-190,共12页Pure and Applied Mathematics

基　　金：国家自然科学基金(12461086);湖北省自然科学基金(2022CFC016).

摘　　要：研究了一类边界条件和转移条件都含有特征参数的Sturm-Liouville问题.首先通过构造一个新的Hilbert空间H和算子A,使得算子A的特征值和所研究问题的特征值一致,得到了算子A是稠密且自共轭的.其次根据Sturm-Liouville方程解的问题,证明了特征值是简单的.We study a class of Sturm-Liouville problems,where both the boundary conditions and transfer conditions involve characteristic parameters.By constructing a new Hilbert space H and an operator A,we find that eigenvalue is consistent with the eigenvalue of the problem studied and the operator A is dense and self-adjoint.Based on the solution problem of the Sturm-Liouville equations,it is proved that the eigenvalues are simple.

关 键 词：STURM-LIOUVILLE问题 转移条件 特征值 

分 类 号：O175.1[理学—数学]