Dependence of Eigenvalues of Certain Closely Discrete Sturm-Liouville Problems
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- 作者：Hao Zhu ; Shurong Sun ; Yuming Shi ; Hongyou Wu
- 关键词：Discrete Sturm ; Liouville problem ; Dependence ; Eigenvalue ; Continuous eigenvalue branch ; Self ; adjoint problem
- 刊名：Complex Analysis and Operator Theory
- 出版年：2016
- 出版时间：April 2016
- 年：2016
- 卷：10
- 期：4
- 页码：667-702
- 全文大小：765 KB
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Shurong Sun (2)
Yuming Shi (1)
Hongyou Wu (3)
1. Department of Mathematics, Shandong University, Jinan, Shandong, 250100, People’s Republic of China
2. School of Mathematical Sciences, University of Jinan, Jinan, Shandong, 250022, People’s Republic of China
3. Department of Mathematics, Northern Illinois University, DeKalb, IL, 60115, USA - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics
Operator Theory
Analysis - 出版者：Birkh盲user Basel
- ISSN：1661-8262
文摘
This paper is concerned with dependence of eigenvalues of certain closely discrete Sturm-Liouville problems. Topologies and geometric structures on various spaces of such problems are firstly introduced. Then, relationships between the analytic and geometric multiplicities of an eigenvalue are discussed. It is shown that all problems sufficiently close to a given problem have eigenvalues near each eigenvalue of the given problem. So, all the simple eigenvalues live in so-called continuous simple eigenvalue branches over the space of problems, and all the eigenvalues live in continuous eigenvalue branches over the space of self-adjoint problems. The analyticity, differentiability and monotonicity of continuous eigenvalue branches are further studied.