非自治二阶哈密顿系统的周期解
Periodic Solutions of Non-Autonomous Second Order Hamiltonian Systems
摘要：
本文推广了M.威廉强迫周期振荡，这需要的假设，强迫潜力是周期性的空间变量。本文仅假设它对时间变量的积分是周期的，从而将结果推广到受迫摆方程。利用直接变分极小化方法和Rabinowtz的鞍点定理，研究了当位势对时间变量的积分为周期时，方程的周期解.
英文摘要：
We try to generalize a result of M. Willem on forced periodic oscillations which required the assumption that the forced potential is periodic on spatial variables. In this paper, we only assume its integral on the time variable is periodic, and so we extend the result to cover the forced pendulum equation. We apply the direct variational minimizing method and Rabinowtz's saddle point theorem to study the periodic solution when the integral of the potential on the time variable is periodic.
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