一类具分布时滞的高阶泛函微分方程的周期解存在性问题(英文)

On the Existence of Periodic Solutions for a Kind of High-order Functional Differential Equation with Distributed Delay

利用Fourier级效理论,伯努利数理论和重合度理论研究了一类具分布时滞的高阶泛函微分方程x^(m)(t)+f(x^(m-1)(t))+g(∫_(-r)~0 x(t+s)da(s))=p(t)的周期解问题,得到了周期解存在的一些新结果。

By using the theory of Fourier series, Bernoulli number theory and continuation theory of coincidence degree theorem, we study a kind of high-order functional differential equation with distributed delay as follows： x^（m）（t）＋f（x^（m-1）（t）＋g（∫-r^0x（t＋s）da（s））=p^（t）Some new results on the existence of periodic solutions are obtained.