二阶无穷时滞泛函微分系统的周期解

非线性二阶泛函微分系统的周期解的存在性是一个十分重要的课题，在工程上有广泛的应用，尤其是Liénard型系统的周期解问题．文章利用重合度理论中的延拓定理和微分积分不等式，研究一类具有单个滞量周期扰动的无穷时滞泛函微分系统T周期解存在性，以Mawhin延拓定理为主要工具证明系统存在T周期解的充分条件，获得的结果具有一定的普遍性．

Periodic Solution for Second Order Functional Differential Equation With Infinite Delay

The existence of periodic solution for second-order nonlinear functional system is an important problem because of its,application in engineering,especially for Liénard system.In the research of the existence of periodic solution for functional differential system,ineutral integral differential system is studied in recent years,and some scholars study the existence of periodic solution for functional equation with infinite delay.By using continuation theorem in coincidence degree and integral differential inequality,we howe studied the existence of periodic solution for second-order functional equation with single quantum disturbance and infinite delay.Sufficient Conditions are obtained for the existence of periodic solutions by using M-awhin theorem,and the result is universal.