A necessary and sufficient condition is established for the existence of periodic solutions of linear impulsive differential equations with distributed delay.

In this paper we consider the dynamics of solutions of impulsive differential equations with fixed time moments of impulsive effects on the basis of comparison methods and vector Lyapunov functions. We propose sufficient conditions on the following dynamic properties: stability, attractivity, and some combinations of them.

The aim of this paper is to prove the existence of periodic piecewise continuous solutions for impulsive planar differential systems having the form of a perturbed Hamiltonian. The proof relies on a continuation technique introduced in [1] and adapted for impulsive equations in [2].