KMS Of Academy of mathematics and systems sciences, CAS
Classification of nonnegative solutions to a bi-harmonic equation with Hartree type nonlinearity | |
Cao, Daomin1,2; Dai, Wei3 | |
2019-08-01 | |
Source Publication | PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS |
ISSN | 0308-2105 |
Volume | 149Issue:4Pages:979-994 |
Abstract | In this paper, we are concerned with the following bi-harmonic equation with Hartree type nonlinearity (P-gamma) Delta(2)u = (1/vertical bar x vertical bar(8) * vertical bar u vertical bar(2)) u(gamma), x is an element of R-d , where 0 < gamma and d >= 9. By the By applying the method of moving planes, we prove that nonnegative classical solutions u to (P.) are radially symmetric about some point x0. Rd and derive the explicit form for u in the. H 2 critical case. = 1. We also prove the non-existence of nontrivial nonnegative classical solutions in the subcritical cases 0 <. < 1. As a consequence, we also derive the best constants and extremal functions in the corresponding Hardy-Littlewood-Sobolev inequalities. |
Keyword | bi-harmonic nonnegative solutions Liouville type theorems radial symmetry Hartree type nonlinearity methods of moving planes |
DOI | 10.1017/prm.2018.67 |
Language | 英语 |
Funding Project | NSFC[11331010] ; NNSF of China[11501021] ; Hua Luo Geng Center of Mathematics, AMSS, CAS |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000490026500008 |
Publisher | CAMBRIDGE UNIV PRESS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/35854 |
Collection | 应用数学研究所 |
Affiliation | 1.Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510405, Guangdong, Peoples R China 2.Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100190, Peoples R China 3.Beihang Univ BUAA, Sch Math & Syst Sci, Beijing 100191, Peoples R China |
Recommended Citation GB/T 7714 | Cao, Daomin,Dai, Wei. Classification of nonnegative solutions to a bi-harmonic equation with Hartree type nonlinearity[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,2019,149(4):979-994. |
APA | Cao, Daomin,&Dai, Wei.(2019).Classification of nonnegative solutions to a bi-harmonic equation with Hartree type nonlinearity.PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,149(4),979-994. |
MLA | Cao, Daomin,et al."Classification of nonnegative solutions to a bi-harmonic equation with Hartree type nonlinearity".PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS 149.4(2019):979-994. |
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