Existence of nonstationary bubbles in higher dimensions

被引：29

作者：

Maris, M ^{[1
]}

机构：

[1] Univ Paris 11, Dept Math, UMR 8628, F-91405 Orsay, France

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2002年 / 81卷 / 12期

关键词：

nonlinear Schrodinger equation; existence of travelling waves; Local Mountain-Pass Theorem; regularity;

D O I：

10.1016/S0021-7824(02)01274-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are interested in the existence of travelling-waves for the nonlinear Schrodinger equation in R-N with "psi(3) - psi(5)"-type nonlinearity. First, we prove an abstract result in critical point theory (a local variant of the classical saddle-point theorem). Using this result, we get the existence of travelling-waves moving with sufficiently small velocity in space dimension N greater than or equal to 4. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

引用

页码：1207 / 1239

页数：33

共 13 条

[1] SOLITON-LIKE BUBBLES IN A SYSTEM OF INTERACTING BOSONS [J].

BARASHENKOV, IV ;

MAKHANKOV, VG .

PHYSICS LETTERS A, 1988, 128 (1-2) :52-56

[2] STABILITY OF THE SOLITON-LIKE BUBBLES [J].

BARASHENKOV, IV ;

GOCHEVA, AD ;

MAKHANKOV, VG ;

PUZYNIN, IV .

PHYSICA D, 1989, 34 (1-2) :240-254

[3]

BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313

[4]

BREZIS H, 1979, J MATH PURE APPL, V58, P137

[5] INSTABILITY OF STATIONARY BUBBLES [J].

DEBOUARD, A .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1995, 26 (03) :566-582

[6]

LIN Z, 1999, SLOW TRAVELLING BUBB

[7]

Lin Z., 2002, Adv. Differ. Equ, V7, P897, DOI [10.57262/ade/1356651683, DOI 10.57262/ADE/1356651683]

[8] UNIQUENESS OF POSITIVE RADIAL SOLUTIONS OF DELTA-U+F(U)=0 IN R(N) .2. [J].

MCLEOD, K .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 339 (02) :495-505

[9] PRINCIPLE OF SYMMETRIC CRITICALITY [J].

PALAIS, RS .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1979, 69 (01) :19-30

[10]

PELETIER LA, 1983, ARCH RATION MECH AN, V81, P181

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