Multiplicity Results on Period Solutions to Higher Dimensional Differential Equations with Multiple Delays
Multiplicity Results on Period Solutions to Higher Dimensional Differential Equations with Multiple Delays
复制标题
DOI：
10.1007/s10884-011-9228-z
复制
发表时间：
2011-09
影响因子：
1.3
通讯作者：
Zhiming Guo;Jianshe Yu
中科院分区：
文献类型：
--
作者：
Zhiming Guo;Jianshe Yu
本文讨论了一类时滞微分方程周期解的存在性和多解性 $$\dot{z}（t）=-f（z（t-1））- f（z（t-2））-\cdots- f（z（t-2n+1））$$其中。利用临界点理论中的S1伪几何指标理论，将Kaplan-Yorke型时滞微分方程的一些已知结果推广到高维情形.结果证明了Kaplan-Yorke猜想在高维系统中成立。
This paper deals with the existence and multiplicity of periodic solutions to delay differential equations of the form $$\dot{z}(t)=-f(z(t-1))- f(z(t-2))-\cdots- f(z(t-2n+1)) $$ where. By using the S 1 pseudo geometrical index theory in the critical point theory, some known results for Kaplan–Yorke type differential delay equations are generalized to higher dimensional case. As a result, the Kaplan–Yorke’s conjecture is proved to be true in the case of higher dimensional systems.