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J. Korean Math. Soc. 2024; 61(3): 445-459
Online first article April 15, 2024 Printed May 1, 2024
https://doi.org/10.4134/JKMS.j230232
Copyright © The Korean Mathematical Society.
Properties of positive solutions for the fractional Laplacian systems with positive-negative mixed powers
Zhongxue Lü, Mengjia Niu, Yuanyuan Shen, Anjie Yuan
Jiangsu Normal University; Jiangsu Normal University; Jiangsu Normal University; Jiangsu Normal University
In this paper, by establishing the direct method of moving planes for the fractional Laplacian system with positive-negative mixed powers, we obtain the radial symmetry and monotonicity of the positive solutions for the fractional Laplacian systems with positive-negative mixed powers in the whole space. We also give two special cases.
Keywords: The fractional Laplacian, positive-negative mixed powers, method of moving planes, radial symmetry, monotonicity
MSC numbers: Primary 35B06, 35B09, 35R11
Supported by: The work was partially supported by NSFC(No.11271166), sponsored by Qing Lan Project.
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