Rotating periodic solutions of second order dissipative dynamical systems

This paper is devoted to the following second order dissipativedynamical system{equation*}u''+cu'+ ∇ g(u)+h(u)=e(t) ~in~R^n.{equation*}When $g(u)=g(|u|)$, ∇ g is a coercive function and h isbounded, we use the coincidence degree theory to obtain someexistence results of rotating periodic solutions, i.e.,$u(t+T)=Qu(t)$, ∀ t∈ 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.