时标线性加权Sturm-Liouville特征值问题的谱理论分析

数学物理学报 ›› 2017, Vol. 37 ›› Issue (3): 427-449.

时标线性加权Sturm-Liouville特征值问题的谱理论分析

罗华

东北财经大学数学学院辽宁大连 116025

收稿日期:2016-05-07 修回日期:2016-10-03 出版日期:2017-06-26 发布日期:2017-06-26
作者简介:罗华,E-mail:luohua@dufe.edu.cn
基金资助:
国家自然科学基金（11301059，71571035）、教育部规划基金（13YJA790078）和辽宁省优秀人才支持计划（LJQ2014128）

Spectral Theory of Linear Weighted Sturm-Liouville Eigenvalue Problems

Luo Hua

Department of Mathematics, Dongbei University of Finance and Economics, Liaoning Dalian 116025

Received:2016-05-07 Revised:2016-10-03 Online:2017-06-26 Published:2017-06-26
Supported by:
Supported by the NSFC (11301059, 71571035), the HSSF of Ministry of Education (13YJA790078) and the Excellent Talents Support Program of Liaoning Province (LJQ2014128)

摘要/Abstract

摘要： 对一类时标线性加权Sturm-Liouville特征值问题，获得了与特征值和特征函数的广义零点分布有关的一些全局结果，建立了Sturm比较定理和Sturm分离定理，同时证明了第一个正特征值和对应正特征函数的存在性.

关键词: 时标, 加权Sturm-Liouville问题, 特征值, 特征函数, 广义零点

Abstract: This paper discusses some global results on eigenvalue and zero distribution for eigenfunction of the linear weighted Sturm-Liouville eigenvalue problem on time scales. We obtain Sturm comparison theorem and Sturm separation theorem and prove the existence of the smallest positive eigenvalue and the corresponding positive eigenfunction.

Key words: Time scales, Weighted Sturm-Liouville problems, Eigenvalues, Eigenfunctions, Generalized zeros

中图分类号:

O175.9

罗华. 时标线性加权Sturm-Liouville特征值问题的谱理论分析[J]. 数学物理学报, 2017, 37(3): 427-449.

Luo Hua. Spectral Theory of Linear Weighted Sturm-Liouville Eigenvalue Problems[J]. Acta mathematica scientia,Series A, 2017, 37(3): 427-449.

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