AbstractIn 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 equationwherer, c:t0,∞) →, R>0 a. e. ont0,∞) and 1/r, c εLl(t0,b) for eachb ∞(t0,>) for somet0>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 o
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