Strong instability of standing waves for a nonlocal Schrodinger equation

被引：54

作者：

Chen, Jianqing

Guo, Boling

机构：

[1] Fujian Normal Univ, Sch Math & Comp Sci, Fuzhou 350007, Peoples R China

[2] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2007年 / 227卷 / 02期

关键词：

variational methods; blow up; strong instability; nonlocal Schrodinger equation; NON-LINEAR SCHRODINGER; CONCENTRATION-COMPACTNESS PRINCIPLE; CAUCHY-PROBLEM; CALCULUS; STATES;

D O I：

10.1016/j.physd.2007.01.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Variational methods are used to prove that the solutions of the nonlocal Schrodinger equation i phi(t)+Delta phi+phi vertical bar phi vertical bar(p-2)(V(x)*vertical bar phi vertical bar(p)) = 0, x is an element of R-N must blow up for a class of initial data with nonnegative energy and some restriction on p. Then using this we prove that the standing wave must be H 1 (RN) strongly unstable with respect to the nonlocal nonlinear Schrodinger equation. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：142 / 148

页数：7

共 16 条

[1]

[Anonymous], 1989, Textos de Metodos Matematicos

[2]

BERESTYCKI H, 1981, CR ACAD SCI I-MATH, V293, P489

[3] ORBITAL STABILITY OF STANDING WAVES FOR SOME NON-LINEAR SCHRODING EQUATIONS [J].