Periodic solutions with prescribed minimal period to Hamiltonian systems

Infinite dimensional hamiltonian systems and nonlinear wave equation: periodic orbits with long minimal period

MULTIPLE PERIODIC SOLUTIONS FOR A CLASS OF NON-AUTONOMOUS AND CONVEX HAMILTONIAN SYSTEMS

In this paper we study Multiple periodic solutions for a class of non-autonomous and convex Hamiltonian systems and we investigate use some properties of Ekeland index.  

Periodic Solutions of Second Order Hamiltonian Systems

We provide sufficient conditions for the existence of periodic solutions of the second order Hamiltonian system −x′′ − λx = εV ′ x (t, x) , where ε is a small parameter, x ∈ R and V (t, x) is 2π-periodic in t. Moreover we provide two applications.

Periodic solutions of even Hamiltonian systems onthe

We consider the Hamiltonian system (HS) ?J _ z = H z (t; z) where H 2 C 2 (R R 2N ; R) is 2-periodic in all variables, so (HS) induces a Hamiltonian system on the torus T 2N. In addition we assume that H is even in the z-variable. This implies the existence of 2 2N trivial stationary solutions of (HS). We are interested in the existence of nontrivial periodic solutions. Observe that the Arnol'd...

On the prescribed - period problem for autonomous Hamiltonian systems ∗

Asymptotically quadratic and subquadratic autonomous Hamiltonian systems are considered. Lower bounds for the number of periodic solutions with a prescribed minimal period are obtained. These bounds are expressed in terms of the numbers of frequencies corresponding to the critical points of the Hamiltonian. Results are based on a global analysis of families of periodic solutions emanating from ...