On stability and instability of standing waves for the nonlinear Schrodinger equation with an inverse-square potential

被引：24

作者：

Bensouilah, Abdelwahab ^{[1
]}

Van Duong Dinh ^{[2
]}

Zhu, Shihui ^{[3
,4
]}

机构：

[1] Univ Lille 1, UFR Math, CNRS, Lab Paul Painleve,UMR 8524, F-59655 Villeneuve Dascq, France

[2] Univ Toulouse, CNRS, UMR5219, Inst Math Toulouse, F-31062 Toulouse 9, France

[3] Sichuan Normal Univ, Dept Math, Chengdu 610066, Peoples R China

[4] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2018年 / 59卷 / 10期

基金：

中国国家自然科学基金;

关键词：

BLOW-UP SOLUTIONS; CRITICAL NLS; SCATTERING;

D O I：

10.1063/1.5038041

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the stability of standing waves for the focusing nonlinear Schrodinger equation with an inverse-square potential. Using the profile decomposition arguments, we show that in the L-2-subcritical case, i.e., 0 < alpha < 4/d, the sets of ground state standing waves are orbitally stable. In the L-2-critical case, i.e., alpha = 4/d, we show that ground state standing waves are strongly unstable by blow-up. Published by AIP Publishing.

引用

页数：18

共 33 条

[1]

Bensouilah A, 2018, ARXIV180408752

[2]

Bensouilah A., 2018, ARXIV180305944

[3]

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

[4] UNIFORM RESOLVENT AND STRICHARTZ ESTIMATES FOR SCHRODINGER EQUATIONS WITH CRITICAL SINGULARITIES [J].

Bouclet, Jean-Marc ;

Mizutani, Haruya .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 370 (10) :7293-7333

[5] A RELATION BETWEEN POINTWISE CONVERGENCE OF FUNCTIONS AND CONVERGENCE OF FUNCTIONALS [J].

BREZIS, H ;

LIEB, E .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (03) :486-490

[6] Strichartz estimates for the wave and Schrodinger equations with the inverse-square potential [J].

Burq, N ;

Planchon, F ;

Stalker, JG ;

Tahvildar-Zadeh, AS .

JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 203 (02) :519-549

[7] Quantum anomaly in molecular physics [J].

Camblong, HE ;

Epele, LN ;

Fanchiotti, H ;

Canal, CAG .

PHYSICAL REVIEW LETTERS, 2001, 87 (22) :art. no.-220402

[8] SINGULAR POTENTIALS [J].

CASE, KM .

PHYSICAL REVIEW, 1950, 80 (05) :797-806

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

CAZENAVE, T ;

LIONS, PL .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 85 (04) :549-561

[10]

Cazenave T, 2003, Semilinear Schrodinger Equations

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