Periodic solutions of some resonant Hamiltonian systems

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...

Periodic Solutions of Spatially Periodic, Even Hamiltonian Systems

Families of Periodic Solutions for Some Hamiltonian PDEs

Abstract. We consider the nonlinear wave equation utt − uxx = ±u and the beam equation utt+uxxxx = ±u on an interval. Numerical observations indicate that time-periodic solutions for these equations are organized into structures that resemble branches and seem to undergo bifurcations. Besides describing our observations, we prove the existence of time-periodic solutions for various periods (a s...