Aubry-Mather Sets for Finite-Twist Maps of a Cylinder and Semilinear Duffing Equations

In this paper, based on a generalized version of the Aubry-Mather theorem about twist maps of an infinite cylinder without the usual infinite twist assumption, we establish the existence of certain quasiperiodic solutions and unlinked periodic solutions in some semilinear Duffing equations where p(t) is a continuous periodic function of period 1 and the semilinearity means that