Period Function for a Class of 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.  

A multiplicity result for a class of superquadratic Hamiltonian systems

We establish the existence of two nontrivial solutions to semilinear elliptic systems with superquadratic and subcritical growth rates. For a small positive parameter λ, we consider the system −∆v = λf(u) in Ω, −∆u = g(v) in Ω, u = v = 0 on ∂Ω, where Ω is a smooth bounded domain in R with N ≥ 1. One solution is obtained applying Ambrosetti and Rabinowitz’s classical Mountain Pass Theorem, and t...

Homoclinic Orbits for a Class of Noncoercive Discrete Hamiltonian Systems

Controllability for a class of discrete-time Hamiltonian systems

In this paper we study the controllability for a class of discrete-time nonlinear systems which arise from a discretization of a continuous-time integrable Hamiltonian systems. We give necessary and sufficient condition for the global controllability of the discrete-time nonlinear systems. The result in this paper are inspired from Ergodic theory. The basic idea is as follows : for the uncontro...

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 ...