With Deviating Arguments Existence Of Solutions For Second Order Functional Differential Equations Cycle

In this paper, by using the abstract continuation theorem of k-set contractive operator, differential inequalities and some analysis techniques, we study the existence of periodic solutions for two kinds of second order functional differential equations with deviating arguments. First, we introduce the abstract continuation theorem of k- set contractive operator; secondly, we study a kind of second order neutral functional differential equations with variable delays and variable coefficients and obtain some sufficient conditions to guarantee the existence of periodic solutions for the equations. The results improve and extend the main results of Huang Xiankai, Xiang Zigui and Wang Genqiang, Yan Jurang. At last, we discuss the existence of periodic solutions for a kind of iterative functional differential equations. Some new results are obtained to guarantee the existence of periodic solutions for the equations. These results improve and extend the corresponding results of Liu Xiping, Jiamei.