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

In this paper, we consider a class of asymptotically linear second‐order Hamiltonian system with resonance at infinity. We will use Morse theory combined with the technique of penalized functionals to obtain the existence of rotating periodic solutions.     

Rotating periodic solutions for second‐order dynamical systems with singularities of repulsive type

In this paper, we study the following second‐order dynamical system: where c ?0 is a constant, and . When g admits a singularity at zero of repulsive type without the restriction of strong force condition, we apply the coincidence degree theory to prove that the system admits nonplanar collisionless rotating periodic solutions taking the form u (t  + T ) = Q u (t ), with T  > 0 and Q an orthogonal matrix under the assumption of Landesman–Lazer type. Copyright © 2016 John Wiley & Sons, Ltd.