  The aim of this paper is to extend previous results regarding the
multiplicity of solutions for quasilinear elliptic problems with critical
growth to the variable exponent case.
  We prove, in the spirit of \cite{DPFBS}, the existence of at least three
nontrivial solutions to the following quasilinear elliptic equation
$-\Delta_{p(x)} u = |u|^{q(x)-2}u +\lambda f(x,u)$ in a smooth bounded domain
$\Omega$ of $\R^N$ with homogeneous Dirichlet boundary conditions on
$\partial\Omega$. We assume that $\{q(x)=p^*(x)\}\not=\emptyset$, where
$p^*(x)=Np(x)/(N-p(x))$ is the critical Sobolev exponent for variable exponents
and $\Delta_{p(x)} u = {div}(|\nabla u|^{p(x)-2}\nabla u)$ is the
$p(x)-$laplacian. The proof is based on variational arguments and the extension
of concentration compactness method for variable exponent spaces.
