In this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.

The paper focuses on the sufficient conditions for oscillatory property to the nonlinear impulsive differential equation(IDE) of the second order with damping term. We submitted a suitable impulsive conditions with the nonlinear equation. The obtained new results in this article generalize and extend some modification results to linear (IDEs) with damping term in the references. We have been given illustrative example to apply the conditions in the main results.

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In this paper, the asymptotic behavior of all solutions of impulsive neutral differential equations with positive and negative coefficients and with impulsive integral term was investigated. Some sufficient conditions were obtained to ensure that all nonoscillatory solutions converge to zero. Illustrative examples were given for the main results.

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