Concentrating standing waves for the fractional Schrodinger equation with critical nonlinearities | |
Li, Suhong1,2; Ding, Yanheng2; Chen, Yu2 | |
2015-12-24 | |
Source Publication | BOUNDARY VALUE PROBLEMS |
ISSN | 1687-2770 |
Pages | 26 |
Abstract | 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. |
Keyword | ground state concentration standing waves nonlocal |
DOI | 10.1186/s13661-015-0507-1 |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000369110600001 |
Publisher | SPRINGER INTERNATIONAL PUBLISHING AG |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/21841 |
Collection | 数学所 |
Affiliation | 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 |
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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