Instability of standing waves of the Schrodinger equation with inhomogeneous nonlinearity

被引：43

作者：

Liu, Y ^{[1
]}

Wang, XP

Wang, K

机构：

[1] Univ Texas, Dept Math, Arlington, TX 76019 USA

[2] Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China

[3] CALTECH, Pasadena, CA 91125 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 358卷 / 05期

关键词：

nonlinear Schrodinger equation; inhomogeneous nonlinearities; blow-up; standing waves; ground state; stability theory;

D O I：

10.1090/S0002-9947-05-03763-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with the inhomogeneous nonlinear Shrodinger equation ( INLS-equation) iu(t) + Delta u + V (epsilon x)vertical bar u vertical bar(p)u = 0, x epsilon R-N. In the critical and supercritical cases p >= 4/N, with N >= 2, it is shown here that standing-wave solutions of ( INLS-equation) on H-1( R-N) perturbation are nonlinearly unstable or unstable by blow-up under certain conditions on the potential term V with a small epsilon > 0.

引用

页码：2105 / 2122

页数：18

共 16 条

[1]

[Anonymous], TEXTOS METODOS MATEM

[2]

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

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