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arXiv · 2202.04002

Liouville type theorems for solutions of the weighted fractional Lane-Emden system

Hatem Hajlaoui
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Abstract

In this paper, we prove Liouville type theorems for stable solutions to the weighted fractional Lane-Emden system \begin{align*} (-\Delta)^s u = h(x)v^p,\quad (-\Delta)^s v= h(x)u^q, \quad u,v>0\quad \mbox{in }\;\mathbb{R}^N, \end{align*} where $1 0$ with $\ell > 0.$ Our results generalize the results established in \cite{HHM16} for the Laplacian case (correspond to $s=1$) and improve the previous work \cite{TuanHoang21}. As a consequence, we prove classification result for stable solutions to the weighted fractional Lane-Emden equation $(-\Delta)^s u = h(x)u^p$ in $\mathbb{R}^N$.

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Hatem Hajlaoui. 2022-02-08. Liouville type theorems for solutions of the weighted fractional Lane-Emden system. https://arxiv.org/abs/2202.04002

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