American Institute of Mathematical Sciences

February  2016, 36(2): 643-652. doi: 10.3934/dcds.2016.36.643

Rotating periodic solutions of second order dissipative dynamical systems

 1 School of Mathematics and Statistics, & Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, China 2 College of Mathematics, Jilin University, Changchun, 130012, China

Received  June 2014 Published  August 2015

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.
Citation: Xiaojun Chang, Yong Li. Rotating periodic solutions of second order dissipative dynamical systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 643-652. doi: 10.3934/dcds.2016.36.643
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