GROUND STATES FOR CHOQUARD EQUATIONS WITH DOUBLY CRITICAL EXPONENTS

被引：14

作者：

Li, Xinfu ^{[1
]}

Ma, Shiwang ^{[2
,3
]}

机构：

[1] Tianjin Univ Commerce, Sch Sci, Tianjin 300134, Peoples R China

[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2019年 / 49卷 / 01期

关键词：

Critical Choquard equation; positive solution; Pohozaev identity; ground state solution; radially symmetric; EXISTENCE;

D O I：

10.1216/RMJ-2019-49-1-153

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, an autonomous Choquard equation with doubly critical exponents is studied. By using the Pohozaev constraint and the perturbed method, a positive and radially symmetric ground state solution in H-1 (R-N) is obtained. The result here extends and complements the earlier theorems obtained by Seok [19] and Moroz and Schaftingen [14].

引用

页码：153 / 170

页数：18

共 25 条

[11] Ground state solution for a class of Schrodinger equations involving general critical growth term [J].

Liu, Jiu ;

Liao, Jia-Feng ;

Tang, Chun-Lei .

NONLINEARITY, 2017, 30 (03) :899-911

[12] Ground states for quasilinear Schrodinger equations with critical growth [J].

Liu, Xiangqing ;

Liu, Jiaquan ;

Wang, Zhi-Qiang .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2013, 46 (3-4) :641-669

[13] A guide to the Choquard equation [J].

Moroz, Vitaly ;

Van Schaftingen, Jean .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2017, 19 (01) :773-813

[14]

Moroz V, 2015, T AM MATH SOC, V367, P6557

[15] Groundstates of nonlinear Choquard equations: Existence, qualitative properties and decay asymptotics [J].

Moroz, Vitaly ;

Van Schaftingen, Jean .

JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 265 (02) :153-184

[16]

Pekar S., 1954, UNTERSUCHUNG ELEKTRO

[17] On gravity's role in quantum state reduction [J].

Penrose, R .

GENERAL RELATIVITY AND GRAVITATION, 1996, 28 (05) :581-600

[18] *LINTEGRALE DE RIEMANN-LIOUVILLE ET LE PROBLEME DE CAUCHY [J].

RIESZ, M .

ACTA MATHEMATICA, 1949, 81 (01) :1-218

[19] Nonlinear Choquard equations: Doubly critical case [J].

Seok, Jinmyoung .

APPLIED MATHEMATICS LETTERS, 2018, 76 :148-156

[20] EXISTENCE OF SOLITARY WAVES IN HIGHER DIMENSIONS [J].

STRAUSS, WA .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1977, 55 (02) :149-162

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