Existence of semiclassical solutions for some critical Dirac equation

doi:10.1063/5.0024707

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	Existence of semiclassical solutions for some critical Dirac equation
	Ding, Yanheng 1,2; Guo, Qi 1,2; Yu, Yuanyang 1,2
	2021
发表期刊	JOURNAL OF MATHEMATICAL PHYSICS
ISSN	0022-2488
卷号	62 期号:1 页码:22
摘要	In this paper, we study the following critical Dirac equation -i epsilon Sigma k=13 alpha k partial derivative ku+a beta u+V(x)u=P(x)f(\|u\|)u+Q(x)\|u\|u, x is an element of R3, where > 0 is a small parameter; a > 0 is a constant; alpha (1), alpha (2), alpha (3), and beta are 4 x 4 Pauli-Dirac matrices; and V, P, Q, and f are continuous but are not necessarily of class C1. We prove the existence and concentration of semiclassical solutions under suitable assumptions on the potentials V(x), P(x), and Q(x) by using variational methods. We also show the semiclassical solutions omega with maximum points x of \|omega \| concentrating at a special set HP characterized by V(x), P(x), and Q(x) and for any sequence x epsilon -> x0 is an element of HP,v epsilon (x):omega epsilon(epsilon x+x epsilon) converges in W1,q(R3,C4) for q >= 2 to a ground state solution u of -i Sigma k=13 alpha k partial derivative ku+a beta u+V(x0)u=P(x0)f(\|u\|)u+Q(x0)\|u\|u,in R3. Finally, we estimate the exponential decay properties of solutions.
DOI	10.1063/5.0024707
收录类别	SCI
语种	英语
资助项目	National Science Foundation of China[NSFC11871242]
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000607170500001
出版者	AMER INST PHYSICS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/57995
专题	中国科学院数学与系统科学研究院
通讯作者	Yu, Yuanyang
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Ding, Yanheng,Guo, Qi,Yu, Yuanyang. Existence of semiclassical solutions for some critical Dirac equation[J]. JOURNAL OF MATHEMATICAL PHYSICS,2021,62(1):22.
APA	Ding, Yanheng,Guo, Qi,&Yu, Yuanyang.(2021).Existence of semiclassical solutions for some critical Dirac equation.JOURNAL OF MATHEMATICAL PHYSICS,62(1),22.
MLA	Ding, Yanheng,et al."Existence of semiclassical solutions for some critical Dirac equation".JOURNAL OF MATHEMATICAL PHYSICS 62.1(2021):22.