Infinite Sharp Conditions by Nehari Manifolds for Nonlinear Schrodinger Equations

被引：4
|
作者：
Lian, Wei [1 ]
Shen, Jihong [2 ]
Xu, Runzhang [1 ,2 ]
Yang, Yanbing [2 ]
机构：
[1] Harbin Engn Univ, Coll Automat, Harbin 150001, Peoples R China
[2] Harbin Engn Univ, Coll Math Sci, Harbin 150001, Peoples R China
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2020年 / 30卷 / 02期
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
Nonlinear Schrodinger equation; Potential wells; Global existence; Blow up; Invariant set; CAUCHY-PROBLEM; ASYMPTOTIC-BEHAVIOR; GLOBAL EXISTENCE; POTENTIAL WELLS; DEEP-WATER; BLOW-UP; SOLITONS;
D O I：
10.1007/s12220-019-00281-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the Cauchy problem of nonlinear Schrodinger equation i phi t+Delta phi+|phi|p-1 phi=0. By constructing infinite Nehari manifolds with geometric features, we not only obtain infinite invariant sets of solutions, but also give infinite sharp conditions for global existence and finite time blow up of solutions.
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页码：1865 / 1886
页数：22
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