Longtime closeness estimates for bounded and unbounded solutions of non-recurrent Duffing equations with polynomial potentials.

In this paper, we consider the Littlewood's problem for the second order differential equation x ¨ + x 2 n + 1 + q (t) x l = p (t) , l < n , where the functions p (t) and q (t) do not need to be periodic. Using the theory of non-periodic twist mappings which is developed by Kunze and Ortega in [3–7] , we obtained longtime closeness results on the bounded and unbounded solutions of the equation. [ABSTRACT FROM AUTHOR]