Electron. J. Diff. Eqns., Vol. 2001(2001), No. 38, pp. 1-17.

Periodic solutions for a class of non-coercive Hamiltonian systems

Morched Boughariou

We prove the existence of non-constant T-periodic orbits of the Hamiltonian system
$\dot q =H_p (t, p(t), q(t))$
$\dot p =-H_q (t, p(t), q(t))$,
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 $\alpha$ greater than
$\beta$ greater than 1.

Submitted January 3, 2001. Published May 28, 2001.
Math Subject Classifications: 34C25, 37J45.
Key Words: Hamiltonian systems, non-coercive, periodic solutions, minimax argument.

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Morched Boughariou
Faculte des Sciences de Tunis
Departement de Mathematiques,
Campus Universitaire, 1060 Tunis, Tunisie
e-mail: Morched.Boughariou@fst.rnu.tn

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