Abstract
In this paper, some sufficient conditions are established for the oscillation of second-order neutral differential equations ( r ( t ) ψ ( x ( t ) ) | Z ′ ( t ) | α - 1 Z ′ ( t ) ) ′ + q ( t ) f ( x ( σ ( t ) ) ) = 0 , t ⩾ t 0 > 0 , where Z ( t ) = x ( t ) + p ( t ) x ( t - τ ) and α > 0 , 0 ⩽ p ( t ) < 1 . On the other hand, some new oscillation criteria are established for the second-order nonlinear neutral delay differential equations [ r ( t ) [ x ( t ) + p ( t ) x ( τ ( t ) ) ] ′ ] ′ + q ( t ) f ( x ( σ ( t ) ) ) = 0 , t ⩾ t 0 > 0 , where ∫ t 0 ∞ d t r ( t ) < ∞ , 0 ⩽ p ( t ) ⩽ p 0 < + ∞ . The results obtained here complement and correct some known results in [1]. Some examples are given to illustrate the main results.
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