The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation

被引：225
|
作者：
Gao, Fashun [1 ]
Yang, Minbo [1 ]
机构：
[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2018年 / 61卷 / 07期
基金：
中国国家自然科学基金;
关键词：
Brezis-Nirenberg problem; Choquard equation; Hardy-Littlewood-Sobolev inequality; critical exponent; CRITICAL SOBOLEV EXPONENTS; GROUND-STATE SOLUTIONS; ELLIPTIC PROBLEMS; SCHRODINGER-EQUATION; EXISTENCE; MULTIPLICITY;
D O I：
10.1007/s11425-016-9067-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation -. u = ( O | u (y)| 2 | x - y | d y) | u | 2 2 u + u in O; where Omega is a bounded domain of R (N) with Lipschitz boundary, lambda is a real parameter, N 3, is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality.
引用
收藏
页码：1219 / 1242
页数：24
相关论文
共 50 条
  • [31] The effect of a perturbation on Brezis-Nirenberg's problem
    Faria, Luiz Fernando de Oliveira
    Silva, Jeferson Camilo
    Ubilla, Pedro
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2024,
  • [32] Positive solutions for a Kirchhoff problem of Brezis-Nirenberg type in dimension four
    Anello, Giovanni
    Vilasi, Luca
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2024, 251
  • [33] Double blow-up solutions for a Brezis-Nirenberg type problem
    Musso, M
    Pistoia, A
    COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2003, 5 (05) : 775 - 802
  • [34] A note on borderline Brezis-Nirenberg type problems
    Haddad, Julian
    Montenegro, Marcos
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 147 : 169 - 175
  • [35] The Brezis-Nirenberg problem near criticality in dimension 3
    del Pino, M
    Dolbeault, J
    Musso, M
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2004, 83 (12): : 1405 - 1456
  • [36] ON QUASILINEAR BREZIS-NIRENBERG TYPE PROBLEMS WITH WEIGHTS
    Garcia-Huidobro, Marta
    Yarer, Cecilia S.
    ADVANCES IN DIFFERENTIAL EQUATIONS, 2010, 15 (5-6) : 401 - 436
  • [37] The solution gap of the Brezis-Nirenberg problem on the hyperbolic space
    Benguria, Soledad
    MONATSHEFTE FUR MATHEMATIK, 2016, 181 (03): : 537 - 559
  • [38] Multispike solutions for the Brezis-Nirenberg problem in dimension three
    Musso, Monica
    Salazar, Dora
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (11) : 6663 - 6709
  • [39] A sharp solvability condition in higher dimensions for some Brezis-Nirenberg type equation
    G. Adimurthi
    K. Mancini
    Calculus of Variations and Partial Differential Equations, 2002, 14 : 275 - 317
  • [40] New numerical solutions for the Brezis-Nirenberg problem on Sn
    Bandle, C
    Stingelin, S
    Elliptic and Parabolic Problems: A SPECIAL TRIBUTE TO THE WORK OF HAIM BREZIS, 2005, 63 : 13 - 21
12345