一阶泛函微分方程变号周期解的存在性

On Sign-changing Periodic Solutions for First Order Functional Differential Equations

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。

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.