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and 

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The main tools for the proofs of our results are following differential equation and inequalities. 

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where 

and 

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The following theorem is a generalization of Theorem 1 in [16] to impulsive delay differential equations with continuous and piecewise constant arguments. 

Theorem 1. ( i ) Inequality (3) has no eventually positive solution if and only if inequality (6) has no eventually positive solution. 

( ii ) Inequality (4) has no eventually negative solution if and only if inequality (7) has no eventually negative solution. 

( iii ) All solutions of the equation (1)-(2) are oscillatory if and only if all solutions of equation (5) are oscillatory. 

Proof. We will prove ( i ) since the proofs of ( ii ) and ( iii ) are similar to proof 

