On the second-order differential equation with piecewise constant argument and almost periodic coefficients Original Research Article

In this paper, we study the existence of almost and quasi-periodic solutions to two classes of second-order differential equations. As a corollary, it is shown that periodic and unbounded solutions can coexist for the equation x″(t)+ω2x(t)=bx([t])+f(t), 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 differential equations with piecewise constant argument. The results are extended to nonlinear equations.