Uniqueness, existence and concentration of positive ground state solutions for Kirchhoff type problems in R-3

doi:10.1016/j.jmaa.2018.01.003

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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
发表期刊	JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN	0022-247X
卷号	461 期号:1 页码:128-149
摘要	In 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.
关键词	Kirchhoff type problems Concentration Schrodinger equation Ground state solution
DOI	10.1016/j.jmaa.2018.01.003
语种	英语
资助项目	National 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研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000426141100009
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29608
专题	数学所
通讯作者	Sun, Dongdong
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 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.