Oscillation criteria of second-order quasi-linear neutral delay differential equations

The oscillatory and non-oscillatory behavior of solutions of the second-order quasi-linear neutral delay differential equation [ a ( t ) | ( x ( t ) + p ( t ) x ( t − τ ) ) ′ | α − 1 ( x ( t ) + p ( t ) x ( t − τ ) ) ′ ] ′ + q ( t ) f ( x ( t − σ ) ) g ( x ′ ( t ) ) = 0 , where t ≥ t 0 , α > 0 , τ ≥ 0 , and σ ≥ 0 are constants, a , q ∈ C ( [ t 0 , ∞ ) ; R ) , p ∈ C 1 ( [ t 0 , ∞ ) ; R ) , f , g ∈ C ( R ; R ) , are studied. Our results generalize and improve some known results of neutral delay differential equations.