Nonoscillation of Second-Order Dynamic Equations with Several Delays

and Applied Analysis 3 In 10 , Leighton proved the following well-known oscillation test for 1.4 ; see 10, 11 . Theorem A see 10 . Assume that ∫∞ t0 1 A0 ( η )dη ∞, ∫∞ t0 A1 ( η ) dη ∞, 1.5 then 1.3 is oscillatory. This result for 1.4 was obtained by Wintner in 12 without imposing any sign condition on the coefficient A1. In 13 , Kneser proved the following result. Theorem B see 13 . Equation 1.4 is nonoscillatory if tA1 t ≤ 1/4 for all t ∈ t0,∞ R, while oscillatory if tA1 t > λ0/4 for all t ∈ t0,∞ R and some λ0 ∈ 1,∞ T. In 14 , Hille proved the following result, which improves the one due to Kneser; see also 14–16 . Theorem C see 14 . Equation 1.4 is nonoscillatory if