Infinitely many solutions of some nonlinear variational equations

The aim of this paper is investigating the existence of one or more critical points of a family of functionals which generalizes the model problem \[\bar J(u) = \int_\Omega \bar A(x,u)|\nabla u|^p dx - \int_\Omega G(x,u) dx\] in the Banach space $W^{1,p}_0(\Omega)\cap L^\infty(\Omega)$, being $\Omega$ a bounded domain in $\R^N$. In order to use ``classical'' theorems, a suitable variant of condition $(C)$ is proved and $W^{1,p}_0(\Omega)$ is decomposed according to a ``good'' sequence of finite dimensional subspaces.