Existence of stable solutions to $(-\mathrm{\Delta }{)}^{m}u=e^u$ in ${\mathbb{R}}^N$ with $m\ge 3$ and $N>2m$

We consider the polyharmonic equation $(-\mathrm{\Delta }{)}^{m}u=e^u$ in ${\mathbb{R}}^N$ with $m\ge 3$ and $N>2m$. We prove the existence of many entire stable solutions. This answer some questions raised by Farina and Ferrero.