考虑具有无限时滞的中立型退化微分系统$$E(t)\frac{\mathrm{d}}{\mathrm{d}t}[x(t)-{\int }_{-\mathrm{\infty }}^{t}C(t,s)x(s)\mathrm{d}s]=A(t)x(t)+f(t,x(t-\tau (t))+b(t)$$ 的周期解的存在性和唯一性问题, 利用线性系统指数型二分性理论和Krasnoselskii不动点定理研究此系统,  并通过技巧性代换获得了保证其周期解存在性和唯一性的充分性条件,
 得到了一些新的结果,推广了相关文献的主要结果.

The periodic solutions to a kind of degenerate differential system with infinite delay of the form E(t) d dt [x(t) −R t−∞ C(t, s)x(s)ds] = A(t)x(t) + f(t, x(t − (t)) + b(t) are considered. By combining the theory of exponential dichotomies of linear system and the theorem of Krasnoselskii, some sufficient conditions that guarantee the existence and uniqueness of periodic solution of the system are obtained.