THE NUMBER OF POSITIVE SOLUTIONS TO THE BREZIS-NIRENBERG PROBLEM
文献类型：期刊论文
| 作者 | Cao, Daomin1,2 ; Luo, Peng3,4; Peng, Shuangjie3,4
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| 刊名 | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000621036100014 |
| 出版者 | AMER MATHEMATICAL SOC |
| 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.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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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