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We study the existence of oscillatory and periodic solutions of a class of first order scalar impulsive delay differential equations with piecewise constant argument.

Abstract. We prove the existence and uniqueness of the solutions of a class of first order nonhomogeneous advanced impulsive differential equations with piecewise constant arguments. We also study the conditions of periodicity, oscillation, nonoscillation and global asymptotic stability for some special cases.

A class of first order linear impulsive differential equation with continuous and piecewise constant arguments is studied. Sufficient conditions for the oscillation of the solutions are obtained.

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We deal with a nonlinear impulsive differential equation system with piecewise constant argument. We prove the existence and uniqueness of a solution. Moreover, we obtain sufficient conditions for the oscillation of the solution.