Rotating periodic solutions of second order dissipative dynamical systems

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

“…Here we modify this idea and gluing two C 1 paths of solutions together to obtain a continuous path of solutions, by which we can track along the trajectory to obtain the rotating periodic solutions (specially, quasi-periodic solutions) of (1.1). For some recent work on rotating periodic solutions of ODEs, one can see [16][17][18][19] and the references.…”

Rotating periodic solutions for asymptotically linear second‐order Hamiltonian systems with resonance at infinity

“…Similar resonance conditions and the technique of penalized functionals were also used to second‐order elliptic equations (see previous studies). Motivated by Chang et al) and Benci et al, in this paper, we present Theorem , giving the existence of nontrivial rotating periodic solutions for . Our resonance conditions (H3) and (H4) are weaker than the resonance condition of Benci et al…”

“…Recently, the existence of rotating periodic solutions for nonlinear differential equations has become a very interesting topic. In 2016, Chang and Li studied the second‐order dissipative dynamical systems, and by using the coincidence degree, they obtained some existence results of rotating periodic solutions. Later, in one study, Chang and Li studied the second‐order dynamical systems with singularities of repulsive type; they proved that the system admits rotating periodic solutions under the assumption of Landesman‐Lazer type by applying the coincidence degree theory.…”

Existence of rotating-periodic solutions for nonlinear second order vector differential equations

“…Recently, the existence of affine-periodic solutions and rotating-periodic solutions for nonlinear differential equations, which was firstly introduced in [24], has become a very interesting topic. Especially, Chang and Li [4,5] studied the existence of rotating-periodic solutions for second order dynamical systems by using the coincidence degree theory. In [21,23], the existence of affine-periodic solutions for nonlinear systems is obtained based on the existence of lower and upper solutions.…”