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

Abstract

We consider the polyharmonic equation $(-\Delta {)}^{m}u=e^u$ 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.

References in corpus (2)

• The Gel'fand problem for the biharmonic operator
• Conformal metrics on ${\mathbb{R}}^{2m}$ with constant Q-curvature

Cited by in corpus (1)

• Qualitative properties of Hénon type equations with exponential nonlinearity