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Classification of nonnegative solutions to a bi-harmonic equation with Hartree type nonlinearity
Cao, Daomin1,2; Dai, Wei3
2019-08-01
Source PublicationPROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
ISSN0308-2105
Volume149Issue:4Pages:979-994
AbstractIn 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.
Keywordbi-harmonic nonnegative solutions Liouville type theorems radial symmetry Hartree type nonlinearity methods of moving planes
DOI10.1017/prm.2018.67
Language英语
Funding ProjectNSFC[11331010] ; NNSF of China[11501021] ; Hua Luo Geng Center of Mathematics, AMSS, CAS
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000490026500008
PublisherCAMBRIDGE UNIV PRESS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35854
Collection应用数学研究所
Corresponding AuthorCao, Daomin
Affiliation1.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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