Existence of quasiperiodic solutions and Littlewood's boundedness problem of Duffing equations with subquadratic potentials

where p(t) is periodic has been extensively investigated due to its relevance in applications. Much work has been carried out concerning the existence of periodic solutions (see [3, 8] also for further references). In this paper we pay attention to more complicated solutions and the Lagrangian stability problem proposed by Littlewood [5]. As remarked in [5], it has been conjectured that all solutions of Eq. (1.1) are bounded if either