Abstract The persistence of periodic, grazing and impact solutions is studied for periodically perturbed ordinary differential equations with impacts. An approach of the Poincare-Adronov-Melnikov method is applied. It is based on introducing and studying an appropriate impact Poincare mapping. Examples are presented to illustrate theoretical results.

中文翻译：

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关于微分方程存在掠射周期解的Poincaré-Adronov-Melnikov方法

摘要 研究了周期性扰动常微分方程的周期性、掠射和撞击解的持久性。应用了 Poincare-Adronov-Melnikov 方法的方法。它基于引入和研究适当的影响庞加莱映射。举例说明理论结果。