一类内部具有不连续性的不定Strum-Liouville算子的非实特征值问题

数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1643-1656.

一类内部具有不连续性的不定Strum-Liouville算子的非实特征值问题

赵迎春^1,*(),孙炯²(),姚斯琴²(),布仁满都拉¹()

¹ 赤峰学院数学与计算机科学学院内蒙古赤峰 024000
² 内蒙古大学数学科学学院呼和浩特 010021

收稿日期:2020-11-09 出版日期:2021-12-26 发布日期:2021-12-02
通讯作者: 赵迎春 E-mail:Yingchun_1983@126.com;masun@imu.edu.cn;89608930@qq.com;brmdllyc@163.com
作者简介:孙炯, E-mail: masun@imu.edu.cn|姚斯琴, E-mail: 89608930@qq.com|布仁满都拉, E-mail: brmdllyc@163.com
基金资助:
国家自然科学基金(11561050);国家自然科学基金(11702038);国家自然科学基金(11801286);内蒙古自然科学基金(2019MS01024)

Non-Real Eigenvalues of a Class of Indefinite Sturm-Liouville Operators with Discontinuity at Interior Points

Yingchun Zhao^1,*(),Jiong Sun²(),Siqin Yao²(), Burenmandula¹()

¹ College of Mathematics and Computer Sciences, Chifeng University, Inner Mongolia Chifeng 024000
² School of Mathematics Sciences, Inner Mongolia University, Hohhot 010021

Received:2020-11-09 Online:2021-12-26 Published:2021-12-02
Contact: Yingchun Zhao E-mail:Yingchun_1983@126.com;masun@imu.edu.cn;89608930@qq.com;brmdllyc@163.com
Supported by:
the NSFC(11561050);the NSFC(11702038);the NSFC(11801286);the NSF of Inner Mongolia Autonomous Region of China(2019MS01024)

摘要/Abstract

摘要：

该文研究了内部具有不连续性的不定Sturm-Liouville算子，首先给出了其特征曲线的解析性质，进而讨论了此类不定问题的非实特征值存在性、个数和上界估计等问题，最后给出了2个具体例子.

关键词: 非实特征值, 转移条件, 特征曲线, 不定的权函数

Abstract:

In this paper, we study indefinite Sturm-Liouville operators with discontinuity at interior point. The analyticity characteristics of the eigencurves is discussed and the sufficient conditions for the existence and exact number and evaluations on the upper bounds for non-real eigenvalues are obtained. Then two examples are given.

Key words: Non-real eigenvalues, Transmission conditions, Eigencurves, Indefinite weight function

中图分类号:

O175.1

赵迎春,孙炯,姚斯琴,布仁满都拉. 一类内部具有不连续性的不定Strum-Liouville算子的非实特征值问题[J]. 数学物理学报, 2021, 41(6): 1643-1656.

Yingchun Zhao,Jiong Sun,Siqin Yao, Burenmandula. Non-Real Eigenvalues of a Class of Indefinite Sturm-Liouville Operators with Discontinuity at Interior Points[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1643-1656.

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