Oscillation of Higher-Order Neutral-Type Periodic Differential Equations with Distributed Arguments

We derive oscillation criteria for general-type neutral differential equations [x(t) +αx(t− τ) +βx(t+ τ)] = δ bax(t − s)dsq1(t,s) + δ ∫ d c x(t + s)dsq2(t,s) = 0, t ≥ t0, where t0 ≥ 0, δ = ±1, τ > 0, b > a ≥ 0, d > c ≥ 0, α and β are real numbers, the functions q1(t,s) : [t0,∞)× [a,b]→R and q2(t,s) : [t0,∞)× [c,d]→R are nondecreasing in s for each fixed t, and τ is periodic and continuous with respect to t for each fixed s. In certain special cases, the results obtained generalize and improve some existing ones in the literature.