Oscillatory behavior of nth-order neutral differential equations with continuous deviating arguments

Oscillatory behavior of the nth-order neutral functional differential equation of the form d d t [ a ( t ){ x ( t )| x ( t )| α − 1 + p ( t ) x ( τ ( t ))} n − 1 ] + δ ∫ c d q ( t , ξ ) f ( x ( σ ( t , ξ ) ) ) d ξ = h ( t ) , δ = ± 1 , is established. Sufficient conditions are provided for the above differential equation to be almost oscillatory in the sense that every solution x(t) of this differential equation is either oscillatory or else limt→∞ |x(t)| = ∞, or lim inft→∞ |x(t)| = 0.