Nonexistence of positive supersolutions to a class of semilinear elliptic equations and systems in an exterior domain

被引：7

作者：

Chen, Huyuan ^{[1
]}

Peng, Rui ^{[2
]}

Zhou, Feng ^{[3
,4
]}

机构：

[1] Jiangxi Normal Univ, Dept Math, Nanchang 330022, Jiangxi, Peoples R China

[2] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

[3] East China Normal Univ, Ctr PDEs, Shanghai 200241, Peoples R China

[4] East China Normal Univ, Sch Math Sci, Shanghai 200241, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2020年 / 63卷 / 07期

基金：

中国国家自然科学基金;

关键词：

semilinear elliptic problem; supersolution; nonexistence; THEOREMS;

D O I：

10.1007/s11425-018-9447-y

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 semilinear elliptic equation:{-Delta u=h(x,u)in omega,u > 0on partial differential omega,where omega is an exterior domain in Double-struck capital R(N)withN > 3,h: omega x Double-struck capital R+-> Double-struck capital R is a measurable function, and derive optimal nonexistence results of positive supersolutions. Our argument is based on a nonexistence result of positive supersolutions of a linear elliptic problem with Hardy potential. We also establish sharp nonexistence results of positive supersolutions to an elliptic system.

引用

页码：1307 / 1322

页数：16

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