  In this work, we prove the existence and multiplicity of positive solutions
for the following class of quasilinear elliptic equations
  $$ \left \{ \begin{array}{lll} -\epsilon^{N}\Delta_{N} u + \left(1+\mu A(x)
\right)\left| u\right|^{N-2}u= f(u)\,\,\,\, \mbox{ in } \, \RR^{N},\\ u > 0
\,\,\,\, \mbox{ in } \, \RR^{N}, \end{array} \right. $$
  \\ where $\Delta_{N}$ is the N-Laplacian operator, $N \geq 2$, $f$ is a
function with exponential critical growth, $\mu$ and $\epsilon$ are positive
parameters and $A$ is a nonnegative continuous function verifying some
hypotheses. To obtain our results, we combine variational arguments and
Lusternik-Schnirelman category theory .
