Liouville-type theorems for fractional Hardy–Hénon systems

被引：0
作者：
Kui Li
Meng Yu
Zhitao Zhang
机构：
[1] Zhengzhou University,School of Mathematics and Statistics
[2] Goethe-Universität Frankfurt,Institut für Mathematik
[3] Chinese Academy of Sciences,HLM, Academy of Mathematics and Systems Science
[4] University of Chinese Academy of Sciences,School of Mathematical Sciences
[5] Jiangsu University,School of Mathematical Sciences
来源：
Nonlinear Differential Equations and Applications NoDEA | 2024年 / 31卷
关键词：
Liouville-type theorem; Fractional-order elliptic system; Hénon-Lane-Emden conjecture; Methods of scaling spheres; Integral system; 35J30; 35J75; 35B53;
D O I：
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摘要：
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 RN\{0}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^N \backslash \{0\}$$\end{document} are also distributional solutions in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^N$$\end{document}. 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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