Existence of quasi-periodic solutions and Littlewood’s boundedness problem of sub-linear impact oscillators Original Research Article

In this paper, it is shown by a series of transformations that how Moser’s invariant curve theorem can be used to analyze the dynamical behavior of sub-linear Duffing-type equations with impact. We prove that all solutions are bounded, and that there are infinitely many periodic and quasi-periodic solutions in this impact case.