The periodic solutions of a class of second order differential equations were studied with the equivalent variational method. By finding suitable transformation, the original second-order periodic boundary value problem was reduced to the first-order periodic boundary value problem in which the periodic solution is more easily obtained. Finally, the application to a class of examples was given to illustrate the potential of this method.%利用等价变分方法研究一类二阶微分方程的周期解问题.通过寻找适当变换,将原来的二阶周期边值问题约化为易于求解的一阶周期边值问题,进而求得周期解.应用实例验证了该方法的有效性.
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