中文摘要：

利用不动点理论，讨论如下方程y（t）=-a（t）y（t）＋f（t,y（t-τ（t）））变号周期解的存在性，给出方程三个非零变号周期解的存在性，其中一个是正的，一个是负的，另一个是变号的。

英文摘要：

In this paper, the existence of sign-changing periodic solutions for first order functional differential equations of the form y（t）=-a（t）y（t）＋f（t,y（t-τ（t））） is considered by using the fixed point theorems. The main results are some new three-solution theorem, which are different from the results in [3,4]. These three solutions are all nonzero. One of them is positive, another is negative, and the third one is a sign-changing solution.