一类边界条件含谱参数的微分算子

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 661-670.

一类边界条件含谱参数的微分算子

孙康,高云兰*()

^{内蒙古工业大学理学院呼和浩特 010051}

收稿日期:2021-05-20 出版日期:2022-06-26 发布日期:2022-05-09
通讯作者: 高云兰 E-mail:Yunlangao20141201@imut.edu.cn
基金资助:
国家自然科学基金(11661059);内蒙古自然科学基金(2017MS(LH)0103)

A Class of Differential Operators with Eigenparameter Dependent Boundary Conditions

Kang Sun,Yunlan Gao*()

^{College of Sciences, Inner Mongolia University of Technology, Hohhot 010051}

Received:2021-05-20 Online:2022-06-26 Published:2022-05-09
Contact: Yunlan Gao E-mail:Yunlangao20141201@imut.edu.cn
Supported by:
the NSFC(11661059);the NSF of Inner Mongolia(2017MS(LH)0103)

摘要/Abstract

摘要：

该文考虑了一类具有转移条件且两个边界条件含谱参数的三阶微分算子, 利用分析法做了两方面的工作, 一是通过构造新空间和新算子将所考虑问题的特征值与新算子的特征值建立联系, 使原问题的特征值和新算子的特征值一致. 二是研究了原问题的特征值的性质, 且给出了原问题的谱只有点谱的结论.

关键词: 微分算子, 边界条件, 转移条件, 特征值

Abstract:

In this paper, A class of third-order differential operators with transition conditions and two boundary conditions containing spectral parameters is studied, and the analytical method is used to do two aspects of work. First, by constructing a new space and a new operator, the eigenvalues of the problem and the operator are connected so that the eigenvalues of the original problem are consistent with the eigenvalues of the new operator. Second, the properties of the eigenvalues of the original problem are studied, and the conclusion that the spectrum of the original problem has only point spectrum is given.

Key words: Differential operator, Boundary condition, Transition condition, Eigenvalues

中图分类号:

O175

孙康,高云兰. 一类边界条件含谱参数的微分算子[J]. 数学物理学报, 2022, 42(3): 661-670.

Kang Sun,Yunlan Gao. A Class of Differential Operators with Eigenparameter Dependent Boundary Conditions[J]. Acta mathematica scientia,Series A, 2022, 42(3): 661-670.

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