THE NUMBER OF POSITIVE SOLUTIONS TO THE BREZIS-NIRENBERG PROBLEM

doi:10.1090/tran/8287

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	THE NUMBER OF POSITIVE SOLUTIONS TO THE BREZIS-NIRENBERG PROBLEM
	Cao, Daomin 3,4; Luo, Peng 1,2; Peng, Shuangjie 1,2
刊名	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
	2021-03-01
卷号	374 期号:3 页码:1947-1985
关键词	Critical Sobolev exponent local Pohozaev identity existence of solutions exact number of solutions Green's function
ISSN号	0002-9947
DOI	10.1090/tran/8287
英文摘要	In this paper we are concerned with the well-known Brezis-Nirenberg problem {-Delta u = u(N+2/N-2) + epsilon u, in Omega, u > 0, in Omega, u = 0, on partial derivative Omega, The existence of multi-peak solutions to the above problem for small epsilon > 0 was obtained by Musso and Pistoia [Indiana Univ. Math. J. 51 (2002), pp. 541-579]). However, the uniqueness or the exact number of positive solutions to the above problem is still unknown. Here we focus on the local uniqueness of multi-peak solutions and the exact number of positive solutions to the above problem for small epsilon > 0. By using various local Pohozaev identities and blow-up analysis, we first detect the relationship between the profile of the blow-up solutions and Green's function of the domain Q and then obtain a type of local uniqueness results of blow-up solutions. Lastly we give a description of the number of positive solutions for small positive epsilon, which depends also on Green's function.
资助项目	Key Project of NSFC[11831009] ; NSFC[11771469] ; NSFC[11701204] ; China Scholarship Council
WOS研究方向	Mathematics
语种	英语
出版者	AMER MATHEMATICAL SOC
WOS记录号	WOS:000621036100014
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58287]
专题	应用数学研究所
通讯作者	Cao, Daomin
作者单位	1.Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China 2.Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 4.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Cao, Daomin,Luo, Peng,Peng, Shuangjie. THE NUMBER OF POSITIVE SOLUTIONS TO THE BREZIS-NIRENBERG PROBLEM[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2021,374(3):1947-1985.
APA	Cao, Daomin,Luo, Peng,&Peng, Shuangjie.(2021).THE NUMBER OF POSITIVE SOLUTIONS TO THE BREZIS-NIRENBERG PROBLEM.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,374(3),1947-1985.
MLA	Cao, Daomin,et al."THE NUMBER OF POSITIVE SOLUTIONS TO THE BREZIS-NIRENBERG PROBLEM".TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 374.3(2021):1947-1985.