A Liouville theorem for the higher-order fractional Laplacian

被引：6
|
作者：
Zhuo, Ran [1 ]
Li, Yan [2 ]
机构：
[1] Huanghuai Univ, Dept Math & Stat, Zhumadian 463000, Henan, Peoples R China
[2] Baylor Univ, Dept Math, Waco, TX 76798 USA
来源：
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2019年 / 21卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Higher-order fractional Laplacian; Green's function; the method of moving planes; symmetry; nonexistence; POSITIVE SOLUTIONS; SYSTEM; CLASSIFICATION; SYMMETRY;
D O I：
10.1142/S0219199718500050
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study Navier problems involving the higher-order fractional Laplacians. We first obtain nonexistence of positive solutions, known as the Liouville-type theorems, in the upper half-space R-+(n) by studying an equivalent integral form of the fractional equation. Then we show symmetry for positive solutions on B-1(0) through a delicate iteration between lower-order differential/pseudo-differential equations split from the higher-order equation.
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页数：19
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