  In this paper, we are concerned with the following elliptic equation
$$\left\{\begin{array}{rrl}-\Delta u&=& |u|^{4/(n-2)}u/[\ln
(e+|u|)]^\varepsilon\hbox{ in } \Omega,\\ u&=&0 \hbox{ on }\partial \Omega,
\end{array} \right.$$ where $\Omega$ is a smooth bounded open domain in
$\mathbb{R}^n, \ n\geq 3$ and $\varepsilon>0$. Clapp et al. in Journal of Diff.
Eq. (Vol 275) proved that there exists a single-peak positive solution for
small $\varepsilon$ if $n \geq 4$. Here we construct positive as well as
changing sign solutions concentrated at several points at the same time.
