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Uniqueness, existence and concentration of positive ground state solutions for Kirchhoff type problems in R-3
Sun, Dongdong; Zhang, Zhitao
2018-05-01
Source PublicationJOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN0022-247X
Volume461Issue:1Pages:128-149
AbstractIn this paper, we first prove the uniqueness of positive ground state solution for the following Kirchhoff equation in R-3 with constant coefficients {- (a + b integral (R3)vertical bar Delta u vertical bar(2))Delta u + cu = d vertical bar u vertical bar(p-1)u in R-3 u > 0, u is an element of H-1(R-3), where a, b, c, d > 0 are positive constants, 3 < p < 5. Then we use the uniqueness result to obtain the existence and concentration theorems of positive ground state solutions to the following Kirchhoff equation with competing potential functions -(epsilon(2)a + epsilon b integral(R3) vertical bar Delta u vertical bar(2))Delta u + V(x)u = K(x)vertical bar u vertical bar(p-1)u in R-3, for a sufficiently small positive parameter epsilon. (C) 2018 Elsevier Inc. All rights reserved.
KeywordKirchhoff type problems Concentration Schrodinger equation Ground state solution
DOI10.1016/j.jmaa.2018.01.003
Language英语
Funding ProjectNational Natural Science Foundation of China[11325107] ; National Natural Science Foundation of China[11271353] ; National Natural Science Foundation of China[11331010] ; National Natural Science Foundation of China[11771428] ; National Natural Science Foundation of China[11688101]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000426141100009
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Cited Times:5[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29608
Collection数学所
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Sun, Dongdong,Zhang, Zhitao. Uniqueness, existence and concentration of positive ground state solutions for Kirchhoff type problems in R-3[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2018,461(1):128-149.
APA Sun, Dongdong,&Zhang, Zhitao.(2018).Uniqueness, existence and concentration of positive ground state solutions for Kirchhoff type problems in R-3.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,461(1),128-149.
MLA Sun, Dongdong,et al."Uniqueness, existence and concentration of positive ground state solutions for Kirchhoff type problems in R-3".JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 461.1(2018):128-149.
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