DIVERGENT SQLUTION TO THE NONLINEAR SCHRODINGER EQUATION WITH THE COMBINED POWER-TYPE NONLINEARITIES

被引：5
|
作者：
Li, Jing [1 ]
Guo, Boling [2 ]
机构：
[1] Changsha Univ Sci & Technol, Sch Math & Comp Sci, Changsha 410114, Hunan, Peoples R China
[2] Inst Appl Phys & Computat Math, Beijing 10088, Peoples R China
来源：
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2017年 / 7卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Nonlinear Schrodinger equation; combined power-type nonlinearities; blow-up; DAVEY-STEWARTSON SYSTEMS; CAUCHY-PROBLEM; BLOW-UP; EXISTENCE; INSTABILITY; SCATTERING; WAVES;
D O I：
10.11948/2017017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the Cauchy problem for the nonlinear Schrodinger equation with combined power-type nonlinearities, which is masscritical/supercr-itical, and energy-subcritical. Combing Du, Wu and Zhang' argument with the variational method, we prove that if the energy of the initial data is negative (or under some more general condition), then the H-1-norm of the solution to the Cauchy problem will go to infinity in some finite time or infinite time.
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页码：249 / 263
页数：15
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