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Abstract

In this paper, we study the existence of almost and quasi periodic solutions to a class of second order delay differential equations. As a corollary, it is shown that the equationcan possess a 4-periodic solution for a 4-periodic function f (t) when b > π 2 or b < 0, which is different from the case: b = 0. This phenomena is due to the piecewise constant argument and illustrates a crucial difference between ordinary differential equations and delay equations with piecewise constant argument. The results are extended to nonlinear equations.