English

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 (Δ)mu=eu(-\Delta)^m u=e^u in RN\mathbb{R}^N with m3m \geq 3 and N>2mN > 2m. 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}
}