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STABLE STANDING WAVES OF NONLINEAR FRACTIONAL SCHRODINGER EQUATIONS
Li, Zaizheng1,2; Zhang, Qidi3; Zhang, Zhitao4,5,6
2022-09-01
Source PublicationCOMMUNICATIONS ON PURE AND APPLIED ANALYSIS
ISSN1534-0392
Pages33
AbstractWe study the existence and orbital stability of standing waves of nonlinear fractional Schrodinger equations with a general nonlinear term iu(t)-(-Delta)(s)u + f(u) = 0, (t,x) is an element of R+ x R-N. We investigate the minimizing problem with L-2 -constraint: E-alpha = inf {1/2 integral(RN) vertical bar(-Delta)(s/2)u vertical bar(2) dx - integral(RN) F(vertical bar u vertical bar)dx vertical bar u is an element of H-s (R-N), parallel to u parallel to(2)(L)(2)((RN )()) = alpha }. The existence and non-existence of global minimizers with respect to E-alpha are established for all possible values of alpha. Under some general assumptions on the nonlinear term f(u), there exists a constant alpha(0) >= 0 such that a global minimizer exists for E-alpha for all alpha > alpha(0), and there is no global minimizer with respect to E-alpha for all 0 < alpha < alpha(0). By virtue of concentration-compactness argument and the strict subadditivity of E-alpha, the strong convergence of minimizing sequence is obtained. Moreover, we present some criteria which determine alpha(0) = 0 or alpha(0) > 0, and the existence of global minimizers for E-alpha 0. Besides, we show the orbital stability of the global minimizers set. Finally, we prove that an energy minimizer is a least action solution by Pohozaev identity.
KeywordFractional Schrodinger equations standing wave orbital stability least action solution
DOI10.3934/cpaa.2022137
Indexed BySCI
Language英语
Funding ProjectNatural Science Foundation of Hebei Province[A2022205007] ; Science and Technology Project of Hebei Education Department[QN2022047] ; Science Foundation of Hebei Normal University[L2021B05] ; National Natural Science Foundation of China[12031015] ; National Natural Science Foundation of China[11771428] ; National Natural Science Foundation of China[12026217]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000859057000001
PublisherAMER INST MATHEMATICAL SCIENCES-AIMS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/61017
Collection中国科学院数学与系统科学研究院
Corresponding AuthorZhang, Qidi
Affiliation1.Hebei Normal Univ, Sch Math Sci, Shijiazhuang, Hebei, Peoples R China
2.Hebei Int Joint Res Ctr Math & Interdisciplinary S, Shijiazhuang 050024, Hebei, Peoples R China
3.Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
4.Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Jiangsu, Peoples R China
5.Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100190, Peoples R China
6.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Li, Zaizheng,Zhang, Qidi,Zhang, Zhitao. STABLE STANDING WAVES OF NONLINEAR FRACTIONAL SCHRODINGER EQUATIONS[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2022:33.
APA Li, Zaizheng,Zhang, Qidi,&Zhang, Zhitao.(2022).STABLE STANDING WAVES OF NONLINEAR FRACTIONAL SCHRODINGER EQUATIONS.COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,33.
MLA Li, Zaizheng,et al."STABLE STANDING WAVES OF NONLINEAR FRACTIONAL SCHRODINGER EQUATIONS".COMMUNICATIONS ON PURE AND APPLIED ANALYSIS (2022):33.
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