Semiclassical states for Choquard type equations with critical growth: critical frequency case

doi:10.1088/1361-6544/aba88d

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	Semiclassical states for Choquard type equations with critical growth: critical frequency case
	Ding, Yanheng 1,2; Gao, Fashun 3; Yang, Minbo 4
	2020-12-01
发表期刊	NONLINEARITY
ISSN	0951-7715
卷号	33 期号:12 页码:6695-6728
摘要	In this paper we are interested in the existence of semiclassical states for the Choquard type equation -epsilon(2)Delta u+V(x)u = (integral(RN)G(u(y))/vertical bar x-y vertical bar(mu)dy) g(u) in R-N, where < mu < N, N >= 3, epsilon is a positive parameter and G is the primitive of g which is of critical growth due to the Hardy-Littlewood-Sobolev inequality. The potential function V(x) is assumed to be nonnegative with V(x) = 0 in some region of R-N, which means it is of the critical frequency case. Firstly, we study a Choquard equation with double critical exponents and prove the existence and multiplicity of semiclassical states by the mountain-pass lemma and the genus theory. Secondly, we consider a class of critical Choquard equation without lower perturbation, by establishing a global compactness lemma for the nonlocal Choquard equation, we prove the multiplicity of high energy semiclassical states by the Lusternik-Schnirelman theory.
关键词	critical Choquard equation semiclassical states critical frequency
DOI	10.1088/1361-6544/aba88d
收录类别	SCI
语种	英语
资助项目	NSFC[11901155] ; ZJNSF[LD19A010001]
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000581522400001
出版者	IOP PUBLISHING LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52305
专题	中国科学院数学与系统科学研究院
通讯作者	Yang, Minbo
作者单位	1.Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Univ Chinese Acad Sci, Chinese Acad Sci, Beijing 100080, Peoples R China 3.Henan Univ Urban Construct, Dept Math & Phys, Pingdingshan 467044, Henan, Peoples R China 4.Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China
推荐引用方式 GB/T 7714	Ding, Yanheng,Gao, Fashun,Yang, Minbo. Semiclassical states for Choquard type equations with critical growth: critical frequency case[J]. NONLINEARITY,2020,33(12):6695-6728.
APA	Ding, Yanheng,Gao, Fashun,&Yang, Minbo.(2020).Semiclassical states for Choquard type equations with critical growth: critical frequency case.NONLINEARITY,33(12),6695-6728.
MLA	Ding, Yanheng,et al."Semiclassical states for Choquard type equations with critical growth: critical frequency case".NONLINEARITY 33.12(2020):6695-6728.