Existence of a ground state and scattering for a nonlinear Schrodinger equation with critical growth

被引：26

作者：

Akahori, Takafumi ^{[1
]}

Ibrahim, Slim ^{[2
]}

Kikuchi, Hiroaki ^{[3
]}

Nawa, Hayato ^{[4
]}

机构：

[1] Shizuoka Univ, Fac Engn, Hamamatsu, Shizuoka 4328561, Japan

[2] Univ Victoria, Dept Math & Stat, Victoria, BC, Canada

[3] Tsuda Coll, Dept Math, Kodaira, Tokyo 1878577, Japan

[4] Osaka Univ, Div Math Sci, Dept Syst Innovat, Grad Sch Engn Sci, Toyonaka, Osaka 5608531, Japan

来源：

SELECTA MATHEMATICA-NEW SERIES | 2013年 / 19卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Nonlinear Schrodinger equation; Scattering problem; Profile decomposition; Virial identity; Variational methods; Ground state; BLOW-UP; INSTABILITY;

D O I：

10.1007/s00029-012-0103-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the energy-critical focusing nonlinear Schrodinger equation with an energy-subcritical perturbation. We show the existence of a ground state in the four or higher dimensions. Moreover, we give a sufficient and necessary condition for a solution to scatter, in the spirit of Kenig and Merle (Invent Math 166:645-675, 2006).

引用

页码：545 / 609

页数：65

共 50 条

[1] Existence of a ground state and scattering for a nonlinear Schrödinger equation with critical growth
Takafumi Akahori
Slim Ibrahim
Hiroaki Kikuchi
Hayato Nawa
Selecta Mathematica, 2013, 19 : 545 - 609
[2] EXISTENCE OF A GROUND STATE AND BLOW-UP PROBLEM FOR A NONLINEAR SCHRODINGER EQUATION WITH CRITICAL GROWTH
Akahori, Takafumi
Ibrahim, Slim
Kikuchi, Hiroaki
Nawa, Hayato
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2012, 25 (3-4) : 383 - 402
[3] Existence of ground state solutions for a quasilinear Schrodinger equation with critical growth
Wu, Ke
Zhou, Fen
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2015, 69 (02) : 81 - 88
[4] Existence of a ground state solution for a nonlinear scalar field equation with critical growth
Alves, Claudianor O.
Souto, Marco A. S.
Montenegro, Marcelo
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2012, 43 (3-4) : 537 - 554
[5] Existence of a ground state solution for a nonlinear scalar field equation with critical growth
Claudianor O. Alves
Marco A. S. Souto
Marcelo Montenegro
Calculus of Variations and Partial Differential Equations, 2012, 43 : 537 - 554
[6] Ground state solutions for a fractional Schrodinger equation with critical growth
Ambrosio, Vincenzo
Figueiredo, Giovany M.
ASYMPTOTIC ANALYSIS, 2017, 105 (3-4) : 159 - 191
[7] Local existence, global existence, and scattering for the nonlinear Schrodinger equation
Cazenave, Thierry
Naumkin, Ivan
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2017, 19 (02)
[8] Existence of ground states for a modified nonlinear Schrodinger equation
Ruiz, David
Siciliano, Gaetano
NONLINEARITY, 2010, 23 (05) : 1221 - 1233
[9] Ground state solution for a Schrodinger-Poisson equation with critical growth
Liu, Jingmei
Qian, Aixia
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2018, 40 : 428 - 443
[10] Existence and concentration of positive solutions for fractional nonlinear Schrodinger equation with critical growth
Shang, Xudong
Zhang, Jihui
JOURNAL OF MATHEMATICAL PHYSICS, 2017, 58 (08)

← 1 2 3 4 5 →