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

Xia Huang; Dong Ye

doi:10.1016/j.jde.2016.01.001

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arXiv · 1509.04314

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

Xia Huang·Dong Ye

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Abstract

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

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Xia Huang, Dong Ye. 2015-09-14. Existence of stable solutions to $(-\Delta)^m u=e^u$ in $\mathbb{R}^N$ with $m \geq 3$ and $N > 2m$. https://doi.org/10.1016/j.jde.2016.01.001

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