Boundedness for sublinear reversible systems with a nonlinear damping and periodic forcing term

In this paper, we are concerned with the sublinear reversible systems with a nonlinear damping and periodic forcing termx″+f(x)g(x′)+γ|x|α−1x=p(t), where f(x), p(t) are odd functions, p(t) is smooth 1-periodic function and γ≠0 is a constant. A sufficient and necessary condition for the boundedness of all solutions of the above equation is established. Moreover, we show the existence of Aubry-Mather sets as well.