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Concentrating standing waves for the fractional Schrodinger equation with critical nonlinearities
Li, Suhong1,2; Ding, Yanheng2; Chen, Yu2
2015-12-24
Source PublicationBOUNDARY VALUE PROBLEMS
ISSN1687-2770
Pages26
AbstractWe 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.
Keywordground state concentration standing waves nonlocal
DOI10.1186/s13661-015-0507-1
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000369110600001
PublisherSPRINGER INTERNATIONAL PUBLISHING AG
Citation statistics
Cited Times:4[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/21841
Collection数学所
Affiliation1.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
Recommended Citation
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.
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