具有周期系数的左定Sturm-Liouville问题的特征值不等式

数学物理学报 ›› 2020, Vol. 40 ›› Issue (2): 340-351.

具有周期系数的左定Sturm-Liouville问题的特征值不等式

孙龙洁(),郝晓玲*(),牛天()

^{内蒙古大学数学科学学院呼和浩特 010021}

收稿日期:2019-06-14 出版日期:2020-04-26 发布日期:2020-05-21
通讯作者: 郝晓玲 E-mail:ljsun0905@163.com;xlhao1883@163.com;396379244@qq.com
作者简介:孙龙洁, E-mail:ljsun0905@163.com|牛天, E-mail:396379244@qq.com
基金资助:
国家自然科学基金(11561050);内蒙古自然科学基金(2018MS01021)

Inequalities Among Eigenvalues of Left-Definite Sturm-Liouville Problems with Periodic Coefficients

Longjie Sun(),Xiaoling Hao*(),Tian Niu()

^{School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021}

Received:2019-06-14 Online:2020-04-26 Published:2020-05-21
Contact: Xiaoling Hao E-mail:ljsun0905@163.com;xlhao1883@163.com;396379244@qq.com
Supported by:
the NSFC(11561050);the NSF of Inner Mongolia(2018MS01021)

摘要/Abstract

摘要：

该文利用了左定问题与右定问题的联系，得到了具有周期系数的左定Sturm-Liouville问题在区间[a，a+kh]上的周期和半周期特征值的描述，阐明了周期特征值之间的不等式关系，并明确给出了区间[a，a+kh]上的周期、半周期特征值和区间[a，a+h]上特征值的一一对应关系.

关键词: 左定Sturm-Liouville问题, 周期系数, 特征值不等式, 一一对应关系

Abstract:

In this paper, by using the relation between left-definite and right-definite problems, the characterization of the periodic and semi-periodic eigenvalues of left-definite Sturm-Liouville problems with periodic coefficients on the interval[a, a+kh] are obtained. For each k >2 we identify explicitly which of the uncountable number of complex conditions generates these periodic eigenvalues. Based on this condition, we give the inequality relation of periodic eigenvalues on the interval[a, a+kh] and 1-1 correspondence between the periodic and semi-periodic eigenvalues on the interval[a, a+kh], k >1 and the corresponding eigenvalues from the interval[a, a+h].

Key words: Left-definite Sturm-liouville problems, Periodic coefficients, Eigenvalues inequalities, 1-1 correspondence

中图分类号:

O175.9

孙龙洁,郝晓玲,牛天. 具有周期系数的左定Sturm-Liouville问题的特征值不等式[J]. 数学物理学报, 2020, 40(2): 340-351.

Longjie Sun,Xiaoling Hao,Tian Niu. Inequalities Among Eigenvalues of Left-Definite Sturm-Liouville Problems with Periodic Coefficients[J]. Acta mathematica scientia,Series A, 2020, 40(2): 340-351.

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