Boundedness and unboundedness of solutions for reversible oscillators at resonance Original Research Article

In this paper we study the problem of boundedness of solutions for the perturbed asymmetric oscillator with damping View the MathML sourceẍ+f(ẋ)+ax+−bx−+g(x)=p(t), Turn MathJax on 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.