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

共 50 条

[11] Some Liouville theorems for Henon type elliptic equations
Wang, Chao
Ye, Dong
JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 262 (04) : 1705 - 1727
[12] Hardy-Henon fractional equation with nonlinearities involving exponential critical growth
Barboza, Eudes M.
Miyagaki, Olimpio H.
Pereira, Fabio R.
Santana, Claudia R.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2025, 28 (01) : 307 - 345
[13] Nontrivial solutions of Hardy-Henon type elliptic systems
Liu, Fang
Yang, Jianfu
ACTA MATHEMATICA SCIENTIA, 2007, 27 (04) : 673 - 688
[14] NONTRIVIAL SOLUTIONS OF HARDY-HENON TYPE ELLIPTIC SYSTEMS
刘芳
杨健夫
Acta Mathematica Scientia, 2007, (04) : 673 - 688
[15] Some weighted fourth-order Hardy-Henon equations
Deng, Shengbing
Tian, Xingliang
JOURNAL OF FUNCTIONAL ANALYSIS, 2023, 284 (01)
[16] Estimate, existence and nonexistence of positive solutions of Hardy-Henon equations
Cheng, Xiyou
Wei, Lei
Zhang, Yimin
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2022, 152 (02) : 518 - 541
[17] Liouville type theorems for poly-harmonic Dirichlet problems of Henon-Hardy type equations on a half space or a ball
Dai, Wei
COLLECTANEA MATHEMATICA, 2023, 74 (03) : 729 - 751
[18] Local behavior of solutions to fractional Hardy-Henon equations with isolated singularity
Li, Yimei
Bao, Jiguang
ANNALI DI MATEMATICA PURA ED APPLICATA, 2019, 198 (01) : 41 - 59
[19] Liouville-Type Theorems for Fractional and Higher-Order Henon-Hardy Type Equations via the Method of Scaling Spheres
Dai, Wei
Qin, Guolin
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023, 2023 (11) : 9001 - 9070
[20] LIOUVILLE THEOREMS FOR HENON TYPE CHOQUARD EQUATION
Dong, Jing
He, Haiyang
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2023, 22 (11) : 3203 - 3217

← 1 2 3 4 5 →