Liouville type theorems for Hardy-Henon equations with concave nonlinearities

被引：12

作者：

Dai, Wei ^{[1
,2
]}

Qin, Guolin ^{[3
,4
]}

机构：

[1] Beihang Univ BUAA, Sch Math & Syst Sci, Beijing 100083, Peoples R China

[2] Univ Paris 13, LAGA, UMR 7539, Paris, France

[3] Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China

[4] Univ Chinese Acad Sci, Beijing 100049, Peoples R China

来源：

MATHEMATISCHE NACHRICHTEN | 2020年 / 293卷 / 06期

基金：

中国国家自然科学基金;

关键词：

bi-harmonic; concave nonlinearity; Hardy-Henon equations; Liouville theorems; nonnegative solutions; super-harmonic property; ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; LOCAL BEHAVIOR; HIGHER-ORDER; CLASSIFICATION;

D O I：

10.1002/mana.201800532

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we are concerned with the Hardy-Henon equations -Delta u=|x|aupand Delta 2u=|x|aupwith a is an element of R and p is an element of(0,1]. Inspired by Serrin and Zou [25], we prove Liouville theorems for nonnegative solutions to the above Hardy-Henon equations (Theorem 1.1 and Theorem 1.3), that is, the unique nonnegative solution is u equivalent to 0.

引用

页码：1084 / 1093

页数：10

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