Multispike Solutions for a slightly subcritical elliptic problem with non-power nonlinearity

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.