Invariant tori and unboundedness for second order differential equations with asymmetric nonlinearities depending on the derivatives

In this paper, the boundedness and unboundedness of solutions of the oscillator x″+ax+−bx−+φ(x)ψ(x′)+f(x)+g(x′)=p(t)x″+ax+−bx−+φ(x)ψ(x′)+f(x)+g(x′)=p(t) are discussed under some suitable conditions.