Boundedness for solutions of nonlinear Hill's equations with periodic forcing terms via Moser's twist theorem

@inproceedings{Bin1989BoundednessFS,
  title={Boundedness for solutions of nonlinear Hill's equations with periodic forcing terms via Moser's twist theorem},
  author={Liu Bin},
  year={1989}
}
We consider the nonlinear Hill's equation with periodic forcing term x′' + βx2n + 1 + (a1 + ea(t))x = p(t), n ⩾ 1, where a(t) and p(t) are continuous and 1-periodic, a1 and β are positive constants, and e is a small parameter. The purpose of this paper is to prove that all solutions of the above-mentioned equation are bounded for t ϵ R and that there are infinitely many quasi-periodic solutions and an infinity of periodic solutions of minimal period m, for each positive integer m.