Rotating periodic solutions of second order dissipative dynamical systems
Rotating periodic solutions of second order dissipative dynamical systems
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DOI：
10.3934/dcds.2016.36.643
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发表时间：
2015-08
影响因子：
1.1
通讯作者：
Xiaojun Chang;Yong Li
中科院分区：
文献类型：
--
作者：
Xiaojun Chang;Yong Li
本文研究了二阶耗散动力系统\开始{方程 *} u“+u "+\nabla g（u）+h（u）=e（t）\mbox{in}\mathbb{R}^n. \end{方程式 *}当$g（u）=g（|u|）$，$\nabla g$是一个强制函数，$h$是有界的，我们利用重合度理论得到了旋转周期解的存在性结果，即$u（t+T）=Qu（t）$，$\for all t\in \mathbb{R}$，其中$T>0$且$Q$为正交矩阵，其中$g$分别为非奇异的和奇异的。特别地，当对g$作了一些强有力的假设时，我们得到了奇异系统非碰撞解的存在性的一些新结果。
This paper is devoted to the following second order dissipative dynamical system \begin{equation*} u''+cu'+ \nabla g(u)+h(u)=e(t) ~\mbox{in}~\mathbb{R}^n. \end{equation*} When $g(u)=g(|u|)$, $\nabla g$ is a coercive function and $h$ is bounded, we use the coincidence degree theory to obtain some existence results of rotating periodic solutions, i.e., $u(t+T)=Qu(t)$, $\forall t\in \mathbb{R}$, with $T>0$ and $Q$ an orthogonal matrix, for $g$ to be nonsingular and singular at zero respectively. Specially, when some strong force type assumption is supposed on $g$, we obtain some new existence results of non-collision solutions for singular systems.