Groundstates of nonlinear Choquard equations: Existence, qualitative properties and decay asymptotics

被引：722

作者：

Moroz, Vitaly ^{[1
]}

Van Schaftingen, Jean ^{[2
]}

机构：

[1] Swansea Univ, Dept Math, Swansea SA2 8PP, W Glam, Wales

[2] Catholic Univ Louvain, Inst Rech Math & Phys, B-1348 Louvain, Belgium

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2013年 / 265卷 / 02期

关键词：

Stationary Choquard equation; Stationary nonlinear Schrodinger-Newton equation; Stationary Hartree equation; Riesz potential; Nonlocal semilinear elliptic problem; Pohozaev identity; Existence; Symmetry; Decay asymptotics; CONCENTRATION-COMPACTNESS PRINCIPLE; SCHRODINGER-EQUATIONS; CALCULUS; SYMMETRY;

D O I：

10.1016/j.jfa.2013.04.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a semilinear elliptic problem -Delta u+u = (I alpha*vertical bar u vertical bar(p))vertical bar u vertical bar(p-2)u R-N, where I-alpha is a Riesz potential and p > 1. This family of equations includes the Choquard or nonlinear Schrodinger Newton equation. For an optimal range of parameters we prove the existence of a positive groundstate solution of the equation. We also establish regularity and positivity of the groundstates and prove that all positive groundstates are radially symmetric and monotone decaying about some point. Finally, we derive the decay asymptotics at infinity of the groundstates. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：153 / 184

页数：32

共 35 条

[11] Semi-classical limit for Schrodinger equations with magnetic field and Hartree-type nonlinearities [J].

Cingolani, Silvia ;

Secchi, Simone ;

Squassina, Marco .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2010, 140 :973-1009

[12] Positive solutions of the nonlinear Schrodinger equation with the fractional Laplacian [J].

Felmer, Patricio ;

Quaas, Alexander ;

Tan, Jinggang .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2012, 142 (06) :1237-1262

[13]

Gidas B., 1981, ADV MATH A S, V7

[14]

Gilbarg D., 1977, Grundlehren der Mathematischen Wissenschaften, V224

[15]

Kavian O., 1993, Introduction a la theorie des points critiques et applications aux problemes elliptiques

[16]

LIEB EH, 1977, STUD APPL MATH, V57, P93

[17]

Lions P. L., 1980, Nonlinear Analysis Theory, Methods & Applications, V4, P1063, DOI 10.1016/0362-546X(80)90016-4

[18]

LIONS PL, 1984, ANN I H POINCARE-AN, V1, P223

[19]

LIONS PL, 1984, ANN I H POINCARE-AN, V1, P109

[20] Classification of Positive Solitary Solutions of the Nonlinear Choquard Equation [J].

Ma, Li ;

Zhao, Lin .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 195 (02) :455-467

← 1 2 3 4 →