THE NUMBER OF POSITIVE SOLUTIONS TO THE BREZIS-NIRENBERG PROBLEM

doi:10.1090/tran/8287

CSpace > 应用数学研究所

	THE NUMBER OF POSITIVE SOLUTIONS TO THE BREZIS-NIRENBERG PROBLEM
	Cao, Daomin1,2 ; Luo, Peng 3,4; Peng, Shuangjie 3,4
	2021-03-01
发表期刊	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN	0002-9947
卷号	374 期号:3 页码:1947-1985
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.
关键词	Critical Sobolev exponent local Pohozaev identity existence of solutions exact number of solutions Green's function
DOI	10.1090/tran/8287
收录类别	SCI
语种	英语
资助项目	Key Project of NSFC[11831009] ; NSFC[11771469] ; NSFC[11701204] ; China Scholarship Council
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000621036100014
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58288
专题	应用数学研究所
通讯作者	Cao, Daomin
作者单位	1.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 3.Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China 4.Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, 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.