  In this paper, we consider the elliptic system \begin{equation*}
  \left\{\begin{array}{ll}
  -\Delta u=g(x,v)\,\, \textnormal{in}\Omega, & \hbox{}
  -\Delta v=f(x,u)\,\,\textnormal{in}\Omega, & \hbox{}
u=v=0\textnormal{on}\partial\Omega, & \hbox{}
  \end{array}
  \right. \end{equation*} where $\Omega$ is a bounded smooth domain in
$\mathbb{R}^N$, and $f$ and $g$ satisfy a general superquadratic condition. By
using variational methods, we prove the existence of infinitely many solutions.
Our argument relies on the application of a generalized variant fountain
theorem for strongly indefinite functionals. Previous results in the topic are
improved.
