  This paper is concerned with the following Euler-Lagrange system \[
  \frac{d}{dt}\mathcal{L}_v(t,u(t),\dot u(t))=\mathcal{L}_x(t,u(t),\dot
u(t))\quad \text{ for a.e. }t\in[-T,T],\quad
  u(-T)=u(T), \] where Lagrangian is given by
$\mathcal{L}=F(t,x,v)+V(t,x)+\langle f(t), x\rangle$, growth conditions are
determined by an anisotropic G-function and some geometric conditions at
infinity. We consider two cases: with and without forcing term $f$. Using a
general version of the Mountain Pass Theorem and Ekeland's variational
principle we prove the existence of at least two nontrivial periodic solutions
in an anisotropic Orlicz-Sobolev space.
