On oscillatory second-order nonlinear delay differential equations of neutral type

In this paper, new sufficient conditions are obtained for oscillation of second-order neutral delay differential equations of the form d d t [ r ( t ) d d t [ x ( t ) + p ( t ) x ( t − τ ) ] ] + q ( t ) G ( x ( t − σ 1 ) ) + v ( t ) H ( x ( t − σ 2 ) ) = 0 , t ≥ t 0 , under the assumptions ∫ ∞ 0 d η r ( η ) = ∞ and ∫ ∞ 0 d η r ( η ) < ∞ for | p ( t ) | < + ∞ . Two illustrative examples are included.