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On the Nonoscillatory Behavior of Solutions of a Second Order Linear Differential Equation
Author(s) -
Li HorngJaan,
Yeh ChehChih
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19961820113
Subject(s) - mathematics , order (exchange) , mathematical proof , comparison theorem , differential equation , pure mathematics , differential (mechanical device) , mathematical analysis , thermodynamics , geometry , physics , finance , economics
In this paper, wo improve the Sturm comparison theorem and two nonoscillation criteria of Leighton and Wintner, and establish two variants of a Wintner' s nonoscillatory criterion of the second order linear differential equationwhere r, c : t 0 ,∞) →, R > 0 a. e. on t 0 ,∞) and 1/r, c ε L l ( t 0 ,b ) for each b ∞ ( t 0 ,>) for some t 0 > 0. Using these two criteria, we improve some nonoscillation criteria of Hartman. Hille. Moore. Potter. WintnEr, and Willett. These proofs are more elegant and concise than those of theirs.