中文摘要：

互惠共存系统的时间周期解在理论和应用中有着重要意义.本文研究了一类具有Holling III功能性反应及非齐次项的互惠共存系统的时间周期解问题.首先利用Galerkin方法构造逼近时间周期解序列,然后利用Leray-Schauder不动点定理和先验估计,证明了逼近时间周期解序列的收敛性,从而得到该系统时间周期解的存在性.

英文摘要：

The time-periodic solution of the mutualistic system has important implications in both theory and application.Discussed in this paper is the time-periodic solution to a mutualistic system with the Holling III type functional response and non-homogeneous terms.The approximate sequence of the time-periodic solution is constructed by using the Galerkin method.Then the convergence of the approximate solution is proved by virtue of the Leray-Schauder fixed point theorem and a priori estimate.Finally,the existence of the time-periodic solution to the discussed mutualistic system is obtained.