一类具偏差变元的高阶泛函微分方程的周期解

Existence of periodic solutions for a kind of higher order functional differential equations with a deviating argument

具有偏差变元的泛函微分方程在生态学和控制论等领域有着广泛的应用。本文利用Mawhin重合度拓展定理和一些分析技巧,研究一类具有偏差变元的高阶泛函微分方程x^(n)(t)+f(x'(t))+h(x(t))x'(t)+g(t,x(t-τ(t)))=p(t),得到了周期解存在新的充分条件,推广了已有的若干结果。

Functional differential equations with deviating arguments have been widely used in fields such as ecology and control theory. By employing the Mawhin coincidence degree theory and some analysis techniques,a kind of higher order functional differential equations with a deviating argument as follows x^（n）（t） ＋ f（ x＇（ t）） ＋ h（ x（ t）） x＇（ t） ＋ g（ t,x（ t- τ（ t））） = p（ t）,is studied,and some sufficient conditions on the existence of periodic solutions is given,which generalizes and improves some known results.