This thesis is intended to be a survey on the comparison theorems and oscillation theorems for second order linear differential equations. We shall discuss four comparison theorems in detail: Sturm-Picone, Levin, Reid and Leighton comparison theorems. For oscillation properties, we shall study Hille-Kneser theorems, and Wintner and Leighton oscillation criteria, which involves analysis of a Riccati equation. In 1969, J.S.W. Wong had some deep results about oscillatory and nonoscillatory differential equations. We shall explain these results and some of the examples in detail.
This survey is mainly based on the monographs of Swanson [12], and Deng [20], plus a paper of Wong [18]. In some places, we give simplifications and extensions.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0111112-005824 |
| Date | 11 January 2012 |
| Creators | Yen, Wen-I |
| Contributors | Wei-Cheng Lian, Chun-Kong Law, Tzon-Tzer Lu |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0111112-005824 |
| Rights | unrestricted, Copyright information available at source archive |
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