Multiplicity results on periodic solutions to higher-dimensional differential equations with multiple delays
Multiplicity results on periodic solutions to higher-dimensional differential equations with multiple delays
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DOI：
10.1216/rmj-2014-44-5-1715
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发表时间：
2014-10
影响因子：
0.8
通讯作者：
B. Zheng;Zhiming Guo
中科院分区：
文献类型：
--
作者：
B. Zheng;Zhiming Guo
本文继续研究一类时滞微分方程周期解的存在性和多解性，
\[
I dot{z}（t）=-f（z（t-l））-f（z（t-2））-I cdots -f（z（t-n + l）），
\]
其中$z\in\br^N$，$f\in C（\br^N，\br^N）$和$n>1$是奇数
number.利用Galerkin近似方法和
临界点理论中的$S^1$-指数理论，一些已知的结果
推广了Kaplan-Yorke型时滞微分方程
更高维的情况。因此，卡普兰-约克猜想
在高维系统中证明是正确的。
This paper continues our study on the existence and multiplicity of periodic solutions to delay differential equations of the form
\[
\dot{z}(t)=-f(z(t-1))-f(z(t-2))-\cdots -f(z(t- n+1)),
\]
where $z\in\br^N$, $f\in C(\br^N, \br^N)$ and $n>1$ is an odd
number. By using the Galerkin approximation method and the
$S^1$-index theory in the critical point theory, some known results
for Kaplan-Yorke type differential delay equations are generalized
to the higher-dimensional case. As a result, the Kaplan-Yorke conjecture
is proved to be true in the case of higher-dimensional systems.