On the Nonoscillatory Behavior of Solutions of a Second Order Linear Differential Equation

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 equation where r, c : t₀,∞) →, R > 0 a. e. on t₀,∞) and 1/r, c ε L^l(t₀,b) for each b ∞ (t₀,>) for some t₀ > 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.