RADIAL SYMMETRY FOR SYSTEMS OF FRACTIONAL LAPLACIAN

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (5): 1567-1582.

RADIAL SYMMETRY FOR SYSTEMS OF FRACTIONAL LAPLACIAN

李从明^1,2, 吴志刚^2,3

1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China;
2. Department of Applied Mathematics, University of Colorado Boulder, USA;
3. Department of Applied Mathematics, Donghua University, Shanghai 201620, China

收稿日期:2018-02-08 出版日期:2018-11-09 发布日期:2018-11-09
通讯作者: Zhigang WU,E-mail:zgwu@dhu.edu.cn E-mail:zgwu@dhu.edu.cn
作者简介:Congming LI,E-mail:congming.li@colorado.edu
基金资助:
Partially supported by NSFC (11571233), NSF DMS-1405175, NSF of Shanghai 16ZR1402100, and China Scholarship Council.

RADIAL SYMMETRY FOR SYSTEMS OF FRACTIONAL LAPLACIAN

Congming LI^1,2, Zhigang WU^2,3

1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China;
2. Department of Applied Mathematics, University of Colorado Boulder, USA;
3. Department of Applied Mathematics, Donghua University, Shanghai 201620, China

Received:2018-02-08 Online:2018-11-09 Published:2018-11-09
Contact: Zhigang WU,E-mail:zgwu@dhu.edu.cn E-mail:zgwu@dhu.edu.cn
Supported by:
Partially supported by NSFC (11571233), NSF DMS-1405175, NSF of Shanghai 16ZR1402100, and China Scholarship Council.

摘要/Abstract

摘要： In this paper, we consider systems of fractional Laplacian equations in Rⁿ with nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We show that there is no positive solution in the subcritical cases, and we classify all positive solutions u_i in the critical cases by using a direct method of moving planes introduced in Chen-Li-Li [11] and some new maximum principles in Li-Wu-Xu [27].

关键词: system of fractional Laplacian, method of moving planes, maximum principles with singular point, Kelvin transform

Abstract: In this paper, we consider systems of fractional Laplacian equations in Rⁿ with nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We show that there is no positive solution in the subcritical cases, and we classify all positive solutions u_i in the critical cases by using a direct method of moving planes introduced in Chen-Li-Li [11] and some new maximum principles in Li-Wu-Xu [27].

Key words: system of fractional Laplacian, method of moving planes, maximum principles with singular point, Kelvin transform

李从明, 吴志刚. RADIAL SYMMETRY FOR SYSTEMS OF FRACTIONAL LAPLACIAN[J]. 数学物理学报(英文版), 2018, 38(5): 1567-1582.

Congming LI, Zhigang WU. RADIAL SYMMETRY FOR SYSTEMS OF FRACTIONAL LAPLACIAN[J]. Acta Mathematica Scientia, 2018, 38(5): 1567-1582.

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RADIAL SYMMETRY FOR SYSTEMS OF FRACTIONAL LAPLACIAN

RADIAL SYMMETRY FOR SYSTEMS OF FRACTIONAL LAPLACIAN

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