Existence of a ground state solution for Choquard equations involving critical Sobolev exponents

被引：0

作者：

Li, Gui-Dong ^{[1
]}

Tang, Chun-Lei ^{[1
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

来源：

ANNALES POLONICI MATHEMATICI | 2019年 / 122卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Choquard equation; Pokhozhaev-Palais-Smale sequence; variational method; positive ground state solution; critical growth; HARDY-LITTLEWOOD-SOBOLEV; SCALAR FIELD-EQUATIONS; SCHRODINGER-EQUATIONS; POSITIVE SOLUTIONS; UNIQUENESS;

D O I：

10.4064/ap180204-23-11

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Choquard equation -Delta u + u = (I-alpha * F(u))f(u) + vertical bar u vertical bar(2)*(-2)u in R-N, where N >= 3, alpha is an element of(0, N), I-alpha is the Riesz potential and F(s) = integral(s)(0) f(t) dt. If f satisfies the general subcritical growth conditions, we obtain the existence of a positive ground state solution by a variational method.

引用

页码：165 / 179

页数：15

共 39 条

[1] Existence of a ground state solution for a nonlinear scalar field equation with critical growth [J].

Alves, Claudianor O. ;

Souto, Marco A. S. ;

Montenegro, Marcelo .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2012, 43 (3-4) :537-554

[2]

BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313

[3] POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS [J].

BREZIS, H ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (04) :437-477

[4]

BREZIS H, 1979, J MATH PURE APPL, V58, P137

[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] Choquard-type equations with Hardy-Littlewood Sobolev upper-critical growth [J].

Cassani, Daniele ;

Zhang, Jianjun .

ADVANCES IN NONLINEAR ANALYSIS, 2019, 8 (01) :1184-1212

[7]

CHABROWSKI J, 1992, REND CIRC MAT PALERM, V41, P413

[8] On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents [J].

Gao, Fashun ;

Yang, Minbo .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 448 (02) :1006-1041

[9]

Gilbarg D., 2001, CLASSICS IN MATH

[10]

Hirata J, 2010, TOPOL METHOD NONL AN, V35, P253

← 1 2 3 4 →