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

In this paper, we are concerned with the following elliptic equation $\left\{\begin{array}{rrl}-Δu&=& |u|^{4/(n-2)}u/[\ln (e+|u|)]^\varepsilon\hbox{ in } Ω,\\ u&=&0 \hbox{ on }\partial Ω, \end{array} \right.$ where $Ω$ 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.

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