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arXiv · 2204.00589

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

Mohamed Ben Ayed·Habib Fourti·Rabeh Ghoudi
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Abstract

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.

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Mohamed Ben Ayed, Habib Fourti, Rabeh Ghoudi. 2022-04-01. Multispike Solutions for a slightly subcritical elliptic problem with non-power nonlinearity. https://arxiv.org/abs/2204.00589

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