Liouville type theorems for nonlinear elliptic equations on extended Grushin manifolds

被引：3

作者：

Tan, Jinggang ^{[1
]}

Yu, Xiaohui ^{[2
]}

机构：

[1] Univ Tecn Federico Santa Maria, Dept Matemat, Avda Espana 1680, Valparaiso, Chile

[2] Shenzhen Univ, Coll Math & Stat, Shenzhen Key Lab Adv Machine Learning & Applicat, Shenzhen 518060, Guangdong, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 269卷 / 01期

关键词：

Liouville type theorem; Moving plane method; Maximum principle; Grushin manifolds; POSITIVE SOLUTIONS; EXTENSION PROBLEM; CLASSIFICATION; SYSTEM;

D O I：

10.1016/j.jde.2019.12.0140022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study two Liouville theorems for nonlinear boundary value problems on extended Grushin manifolds. These problems are closely related to nonlinear fractional Grushin equations. We will prove that these problems do not possess nontrivial positive solution under some assumptions on the nonlinear terms. We use the moving plane method in an integral form to prove our results. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：523 / 541

页数：19

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