Concentrating standing waves for the fractional Schrodinger equation with critical nonlinearities

doi:10.1186/s13661-015-0507-1

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	Concentrating standing waves for the fractional Schrodinger equation with critical nonlinearities
	Li, Suhong 1,2; Ding, Yanheng2 ; Chen, Yu 2
刊名	BOUNDARY VALUE PROBLEMS
	2015-12-24
页码	26
关键词	ground state concentration standing waves nonlocal
ISSN号	1687-2770
DOI	10.1186/s13661-015-0507-1
英文摘要	We study the following nonlocal Schrodinger equations: epsilon(2s)(-Delta)(s)u+V(x)u = W(x)f(u), epsilon(2s)(-Delta)(s)u+V(x)u = W(x)f(u) + u(2s-1)) for u is an element of H-s(R-N), where f (u) is superlinear and subcritical, 2s=2N/N-2s if N>2s. V(x) and W(x) are sufficiently smooth potential with inf V(x) > 0, inf W(x) > 0, and epsilon > 0 is a small number. Under proper assumptions, we explore the existence, concentration phenomenon, convergence, and decay estimate of semiclassical solutions of (I) and (II), respectively. Compared with some existing issues, the most interesting results obtained here are therefore: the concentration phenomenon depends on competing potential functions; the nonlocal critical problem (II) is considered; unlike the classical case s = 1, the decay estimate of solution to (I) or (II) is of polynomial instead of exponential form, due to the nonlocal effect.
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER INTERNATIONAL PUBLISHING AG
WOS记录号	WOS:000369110600001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/21840]
专题	数学所
通讯作者	Li, Suhong
作者单位	1.Hebei Normal Univ Sci & Technol, Inst Math & Informat Technol, Qinhuangdao 066004, Hebei, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Suhong,Ding, Yanheng,Chen, Yu. Concentrating standing waves for the fractional Schrodinger equation with critical nonlinearities[J]. BOUNDARY VALUE PROBLEMS,2015:26.
APA	Li, Suhong,Ding, Yanheng,&Chen, Yu.(2015).Concentrating standing waves for the fractional Schrodinger equation with critical nonlinearities.BOUNDARY VALUE PROBLEMS,26.
MLA	Li, Suhong,et al."Concentrating standing waves for the fractional Schrodinger equation with critical nonlinearities".BOUNDARY VALUE PROBLEMS (2015):26.