New approach for the existence of pseudo almost periodic solutions for some second order differential equation with piecewise constant argument

The following equation d²/dt²(x(t)+px(t-1))=qx(2(t+1)/2])+f(t)${\mathrm{d}}^2/\mathrm{d}{t}^2(x(t)+\mathit{px}(t-1))=\mathit{qx}(2(t+1)/2])+f(t)$ is considered and necessary and sufficient conditions are given in order to ensure the existence and uniqueness of pseudo almost periodic solutions.