SYMMETRY AND NONEXISTENCE OF POSITIVE SOLUTIONS TO FRACTIONAL P-LAPLACIAN EQUATIONS

被引：27
作者：
Wu, Leyun [1 ]
Niu, Pengcheng [1 ]
机构：
[1] Northwestern Polytech Univ, Dept Appl Math, Xian 710129, Shaanxi, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2019年 / 39卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Fractional p-Laplacian equation; narrow region principle; direct method of moving planes; radial symmetry; nonexistence; ELLIPTIC PROBLEM;
D O I：
10.3934/dcds.2019069
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the fractional p-Laplacian equation (-Delta)(p)(s)u(x) = f(u(x)), where the fractional p-Laplacian is of the form (-Delta)(p)(s)u(x) = Cn,s,pPV integral(Rn) vertical bar u(x) - u(y)vertical bar(p-2)(u(x) - u(y))/vertical bar x - y vertical bar(n+sp) dy. By proving a narrow region principle to the equation above and extending the direct method of moving planes used in fractional Laplacian equations, we establish the radial symmetry in the unit ball and nonexistence on the half space for the solutions, respectively.
引用
收藏
页码：1573 / 1583
页数：11
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