Comparison and Oscillation Theorems for Second Order Linear Differential Equations

• Main Authors: Wen-I Yen, 顏玟檍
• Other Authors: Chun-Kong Law
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/52185768920759901327

碩士 === 國立中山大學 === 應用數學系研究所 === 100 === 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.