Orbital stability for the Schrodinger operator involving inverse square potential

被引：14

作者：

Trachanas, Georgios P. ^{[1
]}

Zographopoulos, Nikolaos B. ^{[2
]}

机构：

[1] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

[2] Univ Mil Educ, Hellen Army Acad, Dept Math & Engn Sci, Athens 16673, Greece

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 259卷 / 10期

关键词：

Orbital stability; Standing wave; Schrodinger equation; Inverse square potential; Hardy inequality; Hidden energy; STANDING WAVES; HARDY INEQUALITY; EQUATIONS; EXISTENCE;

D O I：

10.1016/j.jde.2015.06.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove the existence of orbitally stable standing waves for the SchrOdinger operator, involving potential of the form c broken vertical bar x broken vertical bar(-2), 0 <c <= c*, where c* is the best constant in the classical Hardy's inequality. The approach is purely variational and it is based on the precompactness of any minimizing sequence with respect to the associated energy. Moreover, we discuss the presence of a Hardy energy term, in conjunction with the behavior of the standing waves. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：4989 / 5016

页数：28

共 42 条

[1] An improved Hardy-Sobolev inequality in W1,p and its application to Schrodinger operators [J].

Adimurthi ;

Esteban, MJ .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2005, 12 (02) :243-263

[2]

[Anonymous], 1996, MINIMAX THEOREMS

[3] Critical heat kernel estimates for Schrodinger operators via Hardy-Sobolev inequalities [J].

Barbatis, G ;

Filippas, S ;

Tertikas, A .

JOURNAL OF FUNCTIONAL ANALYSIS, 2004, 208 (01) :1-30

[4] On the Orbital Stability for a Class of Nonautonomous NLS [J].

Bellazzini, Jacopo ;

Visciglia, Nicola .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2010, 59 (03) :1211-1230

[5] Nonlinear Schrodinger equations with strongly singular potentials [J].

Bellazzini, Jacopo ;

Bonanno, Claudio .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2010, 140 :707-721

[6] On a semilinear elliptic equation with inverse-square potential [J].

Brezis, Haim ;

Dupaigne, Louis ;

Tesei, Alberto .

SELECTA MATHEMATICA-NEW SERIES, 2005, 11 (01) :1-7

[7] 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

[8]

CAFFARELLI L, 1984, COMPOS MATH, V53, P259

[9]

Cazacu C., ARXIV14096433V1

[10] 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

← 1 2 3 4 5 →