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

Abstract

In this paper we prove the Liouville type theorem for stable at infinity solutions of the following equation $$Δ_{m}^{3}u =|u|^{θ-1}u\;\;\; \mbox{in}\,\, \mathbb{R}^N,$$ 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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