Existence of stable solutions to $(-\Delta)^m u=e^u$ in $\mathbb{R}^N$ with $m \geq 3$ and $N > 2m$
Analysis of PDEs
2016-02-22 v1
Abstract
We consider the polyharmonic equation in with and . We prove the existence of many entire stable solutions. This answer some questions raised by Farina and Ferrero.
Keywords
Cite
@article{arxiv.1509.04314,
title = {Existence of stable solutions to $(-\Delta)^m u=e^u$ in $\mathbb{R}^N$ with $m \geq 3$ and $N > 2m$},
author = {Xia Huang and Dong Ye},
journal= {arXiv preprint arXiv:1509.04314},
year = {2016}
}