中文摘要：

主要研究了带阻尼项的脉冲方程在弱的次线性增长的条件下周期解的存在性问题.首先证明该系统的周期解对应着一个泛函的临界点,从而将周期解的存在性问题转化为寻找该泛函的临界点问题.然后,在弱的次线性条件下,利用鞍点定理,证明了临界点的存在性,从而得到了带阻尼项的脉冲方程在弱的次线性增长的条件下至少存在一个周期解.

英文摘要：

In this study the existence of periodic solutions of impulsive systems was probed with damped term under weak sublinear growth conditions. Firstly the result that the periodic solutions of this system corresponding to the critical points of a functional was proved, and thus the existence problem of periodic solutions was transformed to find the critical points of the functional. The existence of critical points was proved by using the Saddle Point Theorem under the conditions of weak linear growth, that is, there exists at least one periodic solution of the above impulsive systems.