BLOW-UP SOLUTIONS AND STRONG INSTABILITY OF GROUND STATES FOR THE INHOMOGENEOUS NONLINEAR SCHRODINGER EQUATION

被引：10

作者：

Ardila, Alex H. ^{[1
]}

Cardoso, Mykael ^{[2
]}

机构：

[1] Univ Fed Minas Gerais ICEx, ICEx UFMG, Dept Math, Caixa Postal 702, BR-30123970 Belo Horizonte, MG, Brazil

[2] Univ Fed Piaui, CCN, Dept Math, BR-64049550 Teresina, PI, Brazil

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2021年 / 20卷 / 01期

关键词：

Nonlinear Schrodinger equation; global existence; blow-up; stability; STABILITY; WAVES; UNIQUENESS; EXISTENCE;

D O I：

10.3934/cpaa.2020259

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using variational methods we study the stability and strong instability of ground states for the focusing inhomogeneous nonlinear Schrodinger equation (INLS) i partial derivative(t)u +Delta u + vertical bar x vertical bar(-b)vertical bar u vertical bar(p-1) u = 0. We construct two kinds of invariant sets under the evolution flow of (INLS). Then we show that the solution of (INLS) is global and bounded in H-1 (R-N) in the first kind of the invariant sets, while the solution blow-up in finite time in the other invariant set. Consequently, we prove that if the nonlinearity is L-2-supercritical, then the ground states are strongly unstable by blow-up.

引用

页码：101 / 119

页数：19

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