New Oscillation Criteria for Second‐Order Neutral Delay Differential Equations with Positive and Negative Coefficients

We establish the oscillation and asymptotic criteria for the second‐order neutral delay differential equations with positive and negative coefficients having the forms [x(t) + ∑i∈Rci(t)x(αi(t))] ′′ + r(t)[x(t) + ∑i∈Rci(t)x(αi(t))] ′ + ∑i∈Ppi(t)x(βi(t)) − ∑i∈Qqi(t)x(γi(t)) = 0 and [x(t) + ∑i∈Rci(t)x(αi(t))] ′′ + r(t)[x(t) + ∑i∈Rci(t)x(αi(t))] ′ + ∑i∈Ppi(t)x(βi(t)) − ∑i∈Qqi(t)x(γi(t)) = f(t). The obtained new oscillation criteria extend and improve the recent results given in the paperof B. Karpuz et al. (2009).