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) admits rotating periodic solutions with form u(t + T) = Qu(t) for any orthogonal matrix Q when the nonlinearity g admits the Hartman-type condition. MSC: 34B15; 34C25; 65L99

Rotating periodic integrable solutions for second-order differential systems with nonresonance condition

“…In [13], they further studied the multiplicity of rotating periodic solutions for a second-order Hamiltonian systems with combined nonlinearities by using the Fountain Theorem. Li, Chang and Li [14] investigated the rotating periodic problems of a class of second order differential system, by applying on the homotopy continuation method, they proved the existence of this type solutions when the nonlinearity term satisfies the Hartman-type condition.…”