具偏差变元的高阶泛函微分方程的周期解存在性问题  

The EXISTENCE OF PERIODIC SOLUTIONS FOR A KIND OF HIGH-ORDER FUNCTIONAL DIFFERENTIAL EQUATION

作　　者：李晓静[1,2] 鲁世平[2] 

机构地区：[1]江苏技术师范大学数理学院,常州213001 [2]安徽师范大学数学系,芜湖241000

出　　处：《系统科学与数学》2009年第3期367-377,共11页Journal of Systems Science and Mathematical Sciences

基　　金：江苏技术师范学院基金项目(KYY08033);安徽省自然科学基金(050460103);安徽省教育厅自然科学基金重点项目(2005kj031zd)资助.

摘　　要：利用Fourier级数理论,伯努利数理论和重合度理论研究了一类具偏差变元的高阶泛函微分方程x^((m))(t)+sum from i=1 to m-1 a_ix^((i))(t)+f(x(t))+β(t)g(x(t-τ(t)))=p(t)的周期解问题,得到了周期解存在的充分条件,有意义的是函数β(t)可变号.In this paper, by using the theory of Fourier series, Bernoulli number theory and continuation theorem of coincidence degree theory, we study a kind of high-order functional differential equations with a deviating argument is considered. Some new results on the existence of periodic solutions are obtained.

关 键 词：高阶泛函微分方程 重合度 周期解 

分 类 号：O175[理学—数学]