一类非线性项前系数可变号的高阶Duffing方程的周期解存在性问题  

THE EXISTENCE OF PERIODIC SOLUTIONS FOR A KIND OF HIGH-ORDER DUFFING EQUATIONS WITH SIGN-CHANGING COEFFICIENT AHEAD OF NONLINEAR TERM

作　　者：李晓静[1,2] 鲁世平[2] 

机构地区：[1]江苏技术师范学院数理学院,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8期1079-1087,共9页Journal of Systems Science and Mathematical Sciences

基　　金：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(KJ2008A05ZC);江苏技术师范学院青年科研基金项目(KYY08033)资助课题

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)+β(t)g(x(t-τ(t)))=p(t)的周期解问题,得到了周期解存在性的新结论,有意义的是非线性项前的系数β(t)可变号,但是,周期解先验界估计方法与已有工作不同.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 equation with a deviating argument as follows： x（m（t）＋β（t）g（x（t-τ（t）））=p（t）. Some new results on the existence of periodic solutions are obtained. Here the sign of β（t） can be changed. But, the methods to estimate a priori bounds of periodic solutions are different from the corresponding ones of the past. Key words High-order, duffing equation, coincidence degree, periodic solution

关 键 词：高阶 DUFFING方程 重合度 周期解. 

分 类 号：O175[理学—数学]