Rotating periodic solutions of second order dissipative dynamical systems

Xiaojun  Chang; Yong  Li

doi:10.3934/dcds.2016.36.643

Article Contents

2016, Volume 36, Issue 2: 643-652. Doi: 10.3934/dcds.2016.36.643

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Rotating periodic solutions of second order dissipative dynamical systems

Xiaojun Chang^1, and
Yong Li^2,

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

Received: June 2014

Published: May 2017

Abstract / Introduction Related Papers Cited by

Abstract

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.

Keywords:

Rotating periodic solutions,
second order dissipative dynamical systems,
coincidence degree theory.

Mathematics Subject Classification: Primary: 34B15, 34C25; Secondary: 47H11.

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