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

Abstract

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