  In this paper, we obtain existence results of periodic solutions of
hamiltonian systems in the Orlicz-Sobolev space $W^1L^{\Phi}([0,T])$. We employ
the direct method of calculus of variations and we consider a potential
function $F$ satisfying the inequality $|\nabla F(t,x)|\leq b_1(t)
\Phi_0'(|x|)+b_2(t)$, with $b_1, b_2\in L^1$ and certain $N$-functions
$\Phi_0$.
