具有时滞的偏差变元的高阶Lienard型方程周期解的存在性  

Periodic Solutions of a Class of High Order Lienard Equation With Deviating Argument and delay

作　　者：罗烈兴 姚晓洁[2] 

机构地区：[1]柳州市柳江县教育局,广西柳州545100 [2]柳州师范高等专科学校数学与计算机科学系,广西柳州545004

出　　处：《柳州师专学报》2008年第2期133-137,共5页Journal of Liuzhou Teachers College

摘　　要：利用更精确的先验界估计和重合度理论,研究了一类具复杂偏差变元的高阶Lienard型方程ax(2n)(t)+f(x(t-)δ)x′(t-δ)+b(t)x(t-τ(t))+c(t)g(x(t-τ(t)))=p(t)的周期解存在性问题,不要求∫0Tp(t)dt=0,在阻尼项f有界和无界的条件下分别得到了其周期解存在的充分条件,推广和改进已有文献的相关结论.By means of better prior estimate and the coineidenoe degree theory, the paper studies the existenoe of periodic solutions to a kind of high order Lienard equation with deviating argument and delay such as ax^（2n）（t）＋f（x（t-δ））x′（t-δ）＋b（t）x（t-τ（t））＋c（t）g（x（t-τ（t）））=p（t） on conditions that f is bounded or unlxxmded, we obtained the sufficient conditions for existence of the periodic solutions on the ridding the condition of ∫Tp（t）dt =0.. the results have extended and improved the related reports in the literatures.

关 键 词：复杂偏差变元 LIENARD型方程 时滞 周期解 存在性 重合度 

分 类 号：O175.8[理学—数学]