Global well-posedness and scattering for nonlinear Schrodinger equations with combined nonlinearities in the radial case

被引：35
|
作者：
Cheng, Xing [1 ]
Miao, Changxing [2 ]
Zhao, Lifeng [3 ,4 ]
机构：
[1] Hohai Univ, Coll Sci, Nanjing 210098, Jiangsu, Peoples R China
[2] Inst Appl Phys & Computat Math, POB 8009, Beijing 100088, Peoples R China
[3] Univ Sci & Technol China, Wu Wen Tsun Key Lab Math, Hefei 230026, Anhui, Peoples R China
[4] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 261卷 / 06期
关键词：
Nonlinear Schrodinger equation; Combined nonlinearities; Global wellposedness; Scattering; Blowup; BLOW-UP; CAUCHY-PROBLEM; GROUND-STATE; DIMENSIONS; COMPACTNESS; EXISTENCE;
D O I：
10.1016/j.jde.2016.04.031
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the Cauchy problem for the nonlinear Schrodinger equation with combined nonlinearities, one of which is defocusing mass-critical and the other is focusing energy-critical or energy-subcritical. The threshold is given by means of variational argument. We establish the profile decomposition in H-1 (R-d) and then utilize the concentration-compactness method to show the global wellposedness and scattering versus blowup in H-1 (R-d) below the threshold for radial data when d <= 4. (C) 2016 Elsevier Inc. All rights reserved.
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页码：2881 / 2934
页数：54
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