Rotating periodic solutions for second order systems with Hartman-type nonlinearity

Abstract In this paper, by a constructive proof based on the homotopy continuation method, we prove that the second order system x″=g(t,x) $x''=g(t,x)$ admits rotating periodic solutions with form u(t+T)=Qu(t) $u(t+T)=Qu(t)$ for any orthogonal matrix Q when the nonlinearity g admits the Hartman-type condition