author={Jifeng Chu and Meirong Zhang},
  journal={Discrete and Continuous Dynamical Systems},
Using the relation between the Hill's equations and the Ermakov- Pinney equations established by Zhang (27), we will give some interesting lower bounds of rotation numbers of Hill's equations. Based on the Birkhofi normal forms and the Moser twist theorem, we will prove that two classes of nonlinear, scalar, time-periodic, Newtonian equations will have twist periodic solutions, one class being regular and another class being singular. 

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