Periodic solutions to non-autonomous second-order systems

We establish the existence of periodic solution of a class of non-autonomous second-order systems, ẍ+μx+V(t,x)=0, where V(t,x)=(v1(t,x),…,vn(t,x)), if lim|x|→∞vi(t,x)|x|=0,i=1,…,n, uniformly in t and V is bounded below or above for appropriate ranges of μ.