Invariant tori for a reversible oscillator with a nonlinear damping and periodic forcing term

In this paper, the boundedness of all solutions of the oscillatorx″+f(x,x′)+ω2x+ϕ(x)=p(t)x″+f(x,x′)+ω2x+ϕ(x)=p(t)is discussed, where ωω is a positive constant, f(x,y),ϕ(x)f(x,y),ϕ(x) and p(t)p(t) are smooth functions, and p(t)=p(t+2π).p(t)=p(t+2π).