On the second-order differential equation with piecewise constant argument and almost periodic coefficients
Here, the author studies 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 \(x''(t)+\omega^2x(t)=bx([t])+f(t)\), which is different from the case: \(b=0\). This phenomenon is due to the piecewise constant argument and illustrates a crucial difference between ordinary differential equations with piecewise constant argument. The results are extended to nonlinear equations.
scientific article; zbMATH DE number 1880103
scientific article