Existence of semiclassical solutions for some critical Dirac equation

doi:10.1063/5.0024707

	Existence of semiclassical solutions for some critical Dirac equation
	Ding, Yanheng 1,2; Guo, Qi 1,2; Yu, Yuanyang 1,2
刊名	JOURNAL OF MATHEMATICAL PHYSICS
	2021
卷号	62 期号:1 页码:22
ISSN号	0022-2488
DOI	10.1063/5.0024707
英文摘要	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.
资助项目	National Science Foundation of China[NSFC11871242]
WOS研究方向	Physics
语种	英语
出版者	AMER INST PHYSICS
WOS记录号	WOS:000607170500001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/57994]
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.