一类线性项前系数可变号的高阶中立型泛函微分方程的周期解

Existence and Uniqueness of Periodic Solutions for a Kind of High-order Neutral Functional Differential Equation with Sign-changing Coefficient Ahead of Linear Term

利用重合度理论,研究一类线性项前系数可变号的高阶中立型泛函微分方程的周期解存在性问题,得到了其周期解存在唯一性的新结果.有趣的是系数β(t)可变号,推广和改进了已有文献的相关结果.

By employing continuation theorem of coincidence degree theory,this paper studies a kind of high-order neutral functional differential equation with sign-changing coefficient ahead of linear term as follows：（x（t）-cx（t-σ））（m）＋β（t）x′（t）＋α（t）g（t,x（t））=e（t）.Some new results on the existence and uniqueness of periodic solutions are obtained.An interesting thing is that the coefficient β（t） is allowed to change sign.The results have extended and improved the related reports in the literatures.