Existence of a ground state and scattering for a nonlinear Schrödinger equation with critical growth

被引：1
作者：
Takafumi Akahori
Slim Ibrahim
Hiroaki Kikuchi
Hayato Nawa
机构：
[1] Shizuoka University,Faculty of Engineering
[2] University of Victoria,Department of Mathematics and Statistics
[3] Tsuda College,Department of Mathematics
[4] Osaka University,Division of Mathematical Science, Department of System Innovation, Graduate School of Engineering Science
来源：
Selecta Mathematica | 2013年 / 19卷
关键词：
Nonlinear Schrödinger equation; Scattering problem; Profile decomposition; Virial identity; Variational methods; Ground state; 35B40; 35B60; 35Q55;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the energy-critical focusing nonlinear Schrödinger equation with an energy-subcritical perturbation. We show the existence of a ground state in the four or higher dimensions. Moreover, we give a sufficient and necessary condition for a solution to scatter, in the spirit of Kenig and Merle (Invent Math 166:645–675, 2006).
引用
收藏
页码：545 / 609
页数：64
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