Rotating periodic solutions of second order dissipative dynamical systems

Abstract

This paper is devoted to the following second order dissipativedynamical 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 $h$ isbounded, we use the coincidence degree theory to obtain someexistence results of rotating periodic solutions, i.e.,$u(t+T)=Qu(t)$, $\forall t\in \mathbb{R}$, with $T>0$ and $Q$ anorthogonal matrix, for $g$ to be nonsingular and singular at zerorespectively. Specially, when some strong force type assumption issupposed on $g$, we obtain some new existence results of non-collisionsolutions for singular systems.