  In this paper we study the existence of bound states of the following class
of quasilinear problems, \begin{equation*} \left\{ \begin{aligned}
  &-\varepsilon ^p\Delta_pu+V(x)u^{p-1}=f(u)+u^{p^\ast -1},\ u>0,\ \text{in}\
\mathbb{R}^{N},
  &\lim _{|x|\rightarrow \infty }u(x) = 0 , \end{aligned} \right.
\end{equation*} where $\varepsilon>0$ is small, $1<p<N,$ $f$ is a nonlinearity
with general subcritical growth in the Sobolev sense, $p^{\ast } = pN/(N-p)$
and $V$ is a continuous nonnegative potential. By introducing a new set of
hypotheses, our analysis includes the critical frequency case which allows the
potential $V$ to not be necessarily bounded below away from zero. We also study
the regularity and behavior of positive solutions as $|x|\rightarrow \infty$ or
$\varepsilon \rightarrow 0,$ proving that they are uniformly bounded and
concentrate around suitable points of $\mathbb{R}^N,$ that may include local
minima of $V$.
