An application of Moser's twist theorem to superlinear impulsive differential equations (Q1633137)

The authors consider a simple superlinear Duffing equation with impulses. In order to apply Moser's twist theorem, it is needed to ensure that the corresponding Poincaré map is quite close to a standard twist map, but it is not usually achieved due to the existence of impulses. The authors provide two types of impulsive functions which can overcome this problem with different effects on the Poincaré map. In both cases, the authors obtain the boundedness of solutions and the existence of quasiperiodic solutions.