Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 38, pp. 1-17.
Title: Periodic solutions for a class of non-coercive Hamiltonian systems
Author: Morched Boughariou (Faculte des Sciences de Tunis, Tunisie)
Abstract:
We prove the existence of non-constant $T$-periodic
orbits of the Hamiltonian system
$$\displaylines{
\dot q =H_p (t, p(t), q(t))\cr
\dot p =-H_q (t, p(t), q(t)),
}$$
where $H$ is a $T$-periodic function in $t$, non-convex and
non-coercive in $(p,q)$, and has the form
$H(t,p,q)\sim |q|^{\alpha}(|p|^{\beta}-1)$ with $\alpha>\beta>1$.
Submitted January 3, 2001. Published May 28, 2001.
Math Subject Classifications: 34C25, 37J45.
Key Words: Hamiltonian systems; non-coercive; periodic solutions; minimax argument.