Existence of periodic solutions of planar systems

x± = max{±x, 0}, y± = max{±y, 0}, m, n ε N, f(x,y,t), g(x,y,t) are bounded, locally Lipschitz functions of x,y for fixed t ε [0, 2π], 2π-periodic in t, and the following limits existlim⁡x,y→±∞f(x,y,t)=:F±,±(t),lim⁡x,y→±∞g(x,y,t)=:G±,±(t)