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2019 Symmetry and nonexistence results for a fractional Hénon-Hardy system on a half-space
Anh Tuan Duong, Phuong Le
Rocky Mountain J. Math. 49(3): 789-816 (2019). DOI: 10.1216/RMJ-2019-49-3-789

Abstract

We study the fractional Henon-Hardy system \begin{aligned}\begin{cases}(-\Delta )^{s/2} u(x) = |x|^\alpha v^p(x), & x\in \mathbb{R}^n_+, \\(-\Delta )^{s/2} v(x) = |x|^\beta u^q(x), & x\in \mathbb{R}^n_+, \\ u(x)=v(x)=0, & x\in \mathbb{R}^n\setminus \mathbb{R}^n_+,\end{cases}\end{aligned} where $n\ge 2$, $0\lt s\lt 2$, $\alpha ,\beta >-s$ and $p,q\ge 1$. We also consider an equivalent integral system. By using a direct method of moving planes, we prove some symmetry and nonexistence results for positive solutions under various assumptions on $\alpha $, $\beta $, $p$ and $q$.

Citation

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Anh Tuan Duong. Phuong Le. "Symmetry and nonexistence results for a fractional Hénon-Hardy system on a half-space." Rocky Mountain J. Math. 49 (3) 789 - 816, 2019. https://doi.org/10.1216/RMJ-2019-49-3-789

Information

Published: 2019
First available in Project Euclid: 23 July 2019

zbMATH: 07088337
MathSciNet: MR3983301
Digital Object Identifier: 10.1216/RMJ-2019-49-3-789

Subjects:
Primary: 35J57
Secondary: 35B06, 35B09, 35B53

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 3 • 2019
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