DIRECT METHOD OF MOVING PLANES FOR LOGARITHMIC LAPLACIAN SYSTEM IN BOUNDED DOMAINS

被引：15

作者：

Liu, Baiyu ^{[1
]}

机构：

[1] Univ Sci & Technol Beijing, Sch Math & Phys, 30 Xueyuan Rd, Beijing 100083, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Logarithmic Laplacian; direct method of moving planes; radial symmetry; LIOUVILLE TYPE THEOREM; FRACTIONAL LAPLACIAN; INTEGRAL-EQUATIONS; ELLIPTIC PROBLEM; SYMMETRY; CLASSIFICATION; NONEXISTENCE; REGULARITY;

D O I：

10.3934/dcds.2018235

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Chen, Li and Li [Adv. Math., 308(2017), pp. 404-437] developed a direct method of moving planes for the fractional Laplacian. In this paper, we extend their method to the logarithmic Laplacian. We consider both the logarithmic equation and the system. To carry out the method, we establish two kinds of narrow region principle for the equation and the system separately. Then using these narrow region principles, we give the radial symmetry results for the solutions to semi-linear logarithmic Laplacian equations and systems on the ball.

引用

页码：5339 / 5349

页数：11

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