PROPERTY OF SOLUTIONS FOR ELLIPTIC EQUATION INVOLVING THE HIGHER-ORDER FRACTIONAL LAPLACIAN IN R+n

被引：0

作者：

Yu, Mei ^{[1
,2
]}

Zhang, Xia ^{[3
]}

Zhang, Binlin ^{[4
]}

机构：

[1] Northwestern Polytech Univ, Sch Math & Stat, Xian 710129, Peoples R China

[2] Yeshiva Univ, Dept Math, New York, NY 10033 USA

[3] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

[4] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2020年 / 19卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Higher-order fractional Laplacian; Liouville theorem; method of moving planes; monotonicity; POSITIVE SOLUTIONS; LIOUVILLE THEOREM; UNIQUENESS; DIFFUSION; EXISTENCE; SYSTEMS;

D O I：

10.3934/cpaa.2020157

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the following equation with the higher-order fractional Laplacian (-Delta)(s) for s = m + alpha/2: (-Delta)(s )u(x) = f(u(x)), x is an element of R-+(n), where m is an element of N*, 0 < alpha < 2. By developing a narrow region principle in unbounded domain and establishing a equivalence of differential equation and integral equation, together with the method of moving planes, we deduce the monotonicity property of positive solutions and the Liouville theorem of nonnegative solutions.

引用

页码：3597 / 3612

页数：16

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