Unbounded Motions of Perturbed Isochronous Hamiltonian Systems at Resonance

Abstract

Abstract Large amplitude solutions of asymptotically positively homogeneous perturbations of hamiltonians systems at resonance can be unbounded, either in the past, or in the future. We present conditions for boundedness or unboundedness, generalizing in particular the results obtained by Alonso and Ortega [1] for scalar second order equations with asymmetric nonlinearities.