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Liouville theorems for stable at infinity solutions of m-triharmonic equation in $\mathbb{R}^N$

Analysis of PDEs 2019-12-18 v2

Abstract

In this paper we prove the Liouville type theorem for stable at infinity solutions of the following equation Δm3u=uθ1u      \mboxinRN,\Delta_{m}^{3}u =|u|^{\theta-1}u\;\;\; \mbox{in}\,\, \mathbb{R}^N, for 1<m1<θ<θs,m:=N(m1)+3mN3m.1<m-1<\theta<\theta_{s, m}:=\frac{N(m-1)+3m }{N-3m}. Here θs,m\theta_{s, m} is a the classic critical exponent for mm- bi-harmonic equation.

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Cite

@article{arxiv.1803.08436,
  title  = {Liouville theorems for stable at infinity solutions of m-triharmonic equation in $\mathbb{R}^N$},
  author = {Foued Mtiri},
  journal= {arXiv preprint arXiv:1803.08436},
  year   = {2019}
}

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