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

  • *Corresponding author: Hatem Hajlaoui

    *Corresponding author: Hatem Hajlaoui
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  • 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<q\leq p $ and $ h $ is a positive continuous function in $ \mathbb{R}^N $ satisfying $ {\liminf_{|x|\to \infty}}\frac{h(x)}{|x|^\ell} > 0 $ with $ \ell > 0. $ Our results generalize the results established in [23] for the Laplacian case (correspond to $ s = 1 $) and improve the previous work [12]. 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 $.

    Mathematics Subject Classification: Primary: 35J47, 35J15; Secondary: 35B53, 35B35.


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