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

Foued Mtiri

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arXiv · 1803.08436

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

Foued Mtiri

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Abstract

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

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Foued Mtiri. 2018-03-22. Liouville theorems for stable at infinity solutions of m-triharmonic equation in $\mathbb{R}^N$. https://arxiv.org/abs/1803.08436

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