Boundedness and unboundedness of solutions for reversible oscillators at resonance

In this paper we study the problem of boundedness of solutions for the perturbed asymmetric oscillator with damping ẍ+f(ẋ)+ax+−bx−+g(x)=p(t), where (a,b)(a,b) lies on one of the Fučik spectrum curves. Since the system in general is non-Hamiltonian, we have to introduce reversibility assumptions to apply the twist theorem for reversible maps. We then obtain a sharp result concerning the boundedness of all solutions.