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.