On the Existence and Uniqueness of Periodic Solutions of a Kind ofNeutral Integro-Differential Equations
一类中立型积分微分方程周期解的存在性和唯一性

The existence and uniqueness of periodic solutions of neutral integro-differential equations with both continuous and discrete delays of the form $$\frac{\rm d}{{\rm d}t}\Bigx(t)+\sum\limits_{j=1}^{q}e_{j}(t)x(t-\delta_{j}(t))\Big] =A(t,x(t))x(t)+\int_{-\infty}^{t}C(t,s)x(s){\rm d}s+\sum\limits_{i=1}^{l}g_{i}(t,x(t-\tau_{i}(t)))+b(t),$$ $$\frac{\rm d}{{\rm d}t}\Bigx(t)+\sum\limits_{j=1}^{q}e_{j}(t)x(t-\delta_{j}(t))\Big]= A(t)x(t)+\int_{-\infty}^{t}C(t,s)x(s){\rm d}s+\sum\limits_{i=1}^{l}g_{i}(t,x(t-\tau_{i}(t)))+b(t)$$are considered. By combining the theory of exponential dichotomies of linear system and the method of functional analysis, some sufficient conditions that guarantee the existence and uniqueness of periodic solution of the system are obtained.