分数 Hardy-Hénon 系统的 Liouville 型定理

Kui Li, Meng Yu, Zhitao Zhang
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摘要

在本文中,我们研究了带权重的分数哈代-赫农椭圆系统的 Liouville 型定理。因为权重在零点是奇异的,所以我们首先证明在 \({\mathbb {R}}^N \backslash \{0\}\)中系统的经典解也是\({\mathbb {R}}^N\) 中的分布解。然后,我们研究了分数哈代-赫农系统与适当积分系统之间的等价性,并通过积分估计和缩放球的方法分别得到了超解和解的新的刘维尔型定理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Liouville-type theorems for fractional Hardy–Hénon systems

In this paper, we study Liouville-type theorems for fractional Hardy–Hénon elliptic systems with weights. Because the weights are singular at zero, we firstly prove that classical solutions for systems in \({\mathbb {R}}^N \backslash \{0\}\) are also distributional solutions in \({\mathbb {R}}^N\). Then we study the equivalence between the fractional Hardy–Hénon system and a proper integral system, and we obtain new Liouville-type theorems for supersolutions and solutions by the method of integral estimates and scaling spheres respectively.

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