Stability of standing waves for the fractional Schrodinger-Hartree equation

被引：60
作者：
Feng, Binhua [1 ]
Zhang, Honghong [1 ]
机构：
[1] Northwest Normal Univ, Dept Math, Lanzhou 780070, Gansu, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 460卷 / 01期
关键词：
Fractional Schrodinger-Hartree equation; Generalized Gagliardo-Nirenberg inequality; Orbital stability of standing waves; CONCENTRATION-COMPACTNESS PRINCIPLE; CAUCHY-PROBLEM; SOLITON DYNAMICS; BLOW-UP; INSTABILITY; EXISTENCE; CALCULUS;
D O I：
10.1016/j.jmaa.2017.11.060
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the stability of standing waves for the fractional Schrodinger-Hartree equation. By using the profile decomposition theory and variational methods, we firstly obtain the best constant of a generalized Gagliardo-Nirenberg inequality and then prove that the standing waves are orbitally stable. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：352 / 364
页数：13
相关论文
共 27 条
[1]   Soliton dynamics for the generalized Choquard equation [J].
Bonanno, Claudio ;
d'Avenia, Pietro ;
Ghimenti, Marco ;
Squassina, Marco .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 417 (01) :180-199
[2]   Blowup for fractional NLS [J].
Boulenger, Thomas ;
Himmelsbach, Dominik ;
Lenzmann, Enno .
JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 271 (09) :2569-2603
[3]  
Cazenave T, 2003, Semilinear Schrodinger Equations
[4]   Strong instability of standing waves for a nonlocal Schrodinger equation [J].
Chen, Jianqing ;
Guo, Boling .
PHYSICA D-NONLINEAR PHENOMENA, 2007, 227 (02) :142-148
[5]   On finite time blow-up for the mass-critical Hartree equations [J].
Cho, Yonggeun ;
Hwang, Gyeongha ;
Kwon, Soonsik ;
Lee, Sanghyuk .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2015, 145 (03) :467-479
[6]   WELL-POSEDNESS AND ILL-POSEDNESS FOR THE CUBIC FRACTIONAL SCHRODINGER EQUATIONS [J].
Cho, Yonggeun ;
Hwang, Gyeongha ;
Kwon, Soonsik ;
Lee, Sanghyuk .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2015, 35 (07) :2863-2880
[7]   ON THE ORBITAL STABILITY OF FRACTIONAL SCHRODINGER EQUATIONS [J].
Cho, Yonggeun ;
Hajaiej, Hichem ;
Hwang, Gyeongha ;
Ozawa, Tohru .
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2014, 13 (03) :1267-1282
[8]   On the Cauchy Problem of Fractional Schrodinger Equation with Hartree Type Nonlinearity [J].
Cho, Yonggeun ;
Hajaiej, Hichem ;
Hwang, Gyeongha ;
Ozawa, Tohru .
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2013, 56 (02) :193-224
[9]   Profile decompositions and blowup phenomena of mass critical fractional Schrodinger equations [J].
Cho, Yonggeun ;
Hwang, Gyeongha ;
Kwon, Soonsik ;
Lee, Sanghyuk .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 86 :12-29
[10]   On fractional Choquard equations [J].
d'Avenia, Pietro ;
Siciliano, Gaetano ;
Squassina, Marco .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2015, 25 (08) :1447-1476
123