Abstract
We study second order linear Sturm-Liouville problems which involve one or two multi-point boundary conditions. Conditions for the existence of a sequence of positive eigenvalues with consecutive zero counts of the eigenfunctions are derived. We also show that these eigenvalues are algebraically simple. Moreover, we obtain certain interlacing relations between the eigenvalues of Sturm-Liouville problems with multi-point boundary conditions and those with two-point separated boundary conditions. The work for multi-point Sturm-Liouville problems will set up a foundation for the further studies of nonlinear boundary value problems with multi-point boundary conditions.
| Original language | English |
|---|---|
| Pages (from-to) | 1167-1179 |
| Journal | Mathematische Nachrichten |
| Volume | 286 |
| Issue number | 11-12 |
| Online published | 28 Feb 2013 |
| DOIs | |
| Publication status | Published - Aug 2013 |
Bibliographical note
Full text of this publication does not contain sufficient affiliation information. The Research Unit(s) information for this record is based on the then academic department affiliation of the author(s).Funding
The research of the second named author was supported in part by the NNSF of China (No. 10971231), and the research of the third one was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 5012/.10P).
Research Keywords
- Sturm-Liouville problems
- existence of eigenvalues
- multiplicities of eigenvalues
- interlacing relations
- NODAL SOLUTIONS
- M-POINT
- 2ND-ORDER
- EIGENVALUES
- EXISTENCE
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