Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity

被引：3
|
作者：
Luo, Huxiao [1 ]
Li, Shengjun [2 ]
Li, Chunji [3 ]
机构：
[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China
[2] Hainan Univ, Coll Informat Sci & Technol, Haikou 570228, Hainan, Peoples R China
[3] Northeastern Univ, Dept Math, Shenyang 110004, Liaoning, Peoples R China
来源：
MATHEMATICS | 2019年 / 7卷 / 02期
基金：
中国国家自然科学基金; 芬兰科学院;
关键词：
variational methods; fractional Choquard equation; ground state solution; vanishing potential; EXISTENCE;
D O I：
10.3390/math7020151
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study a class of nonlinear Choquard equation driven by the fractional Laplacian. When the potential function vanishes at infinity, we obtain the existence of a ground state solution for the fractional Choquard equation by using a non-Nehari manifold method. Moreover, in the zero mass case, we obtain a nontrivial solution by using a perturbation method. The results improve upon those in Alves, Figueiredo, and Yang (2015) and Shen, Gao, and Yang (2016).
引用
收藏
页数：17
相关论文
共 50 条
  • [31] Ground State Solutions for a Class of Strongly Indefinite Choquard Equations
    Claudianor O. Alves
    Huxiao Luo
    Minbo Yang
    Bulletin of the Malaysian Mathematical Sciences Society, 2020, 43 : 3271 - 3304
  • [32] Ground State Solutions for a Class of Strongly Indefinite Choquard Equations
    Alves, Claudianor O.
    Luo, Huxiao
    Yang, Minbo
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2020, 43 (04) : 3271 - 3304
  • [33] Fractional magnetic Schrodinger equations with potential vanishing at infinity and supercritical exponents
    de Albuquerque, J. C.
    Santos, J. L.
    COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2024, 69 (12) : 2094 - 2117
  • [34] On existence and concentration behavior of positive ground state solutions for a class of fractional Schrodinger-Choquard equations
    Gao, Zu
    Tang, Xianhua
    Chen, Sitong
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2018, 69 (05):
  • [35] On existence and concentration behavior of positive ground state solutions for a class of fractional Schrödinger–Choquard equations
    Zu Gao
    Xianhua Tang
    Sitong Chen
    Zeitschrift für angewandte Mathematik und Physik, 2018, 69
  • [36] Infinitely many solutions for fractional Schrodinger equation with potential vanishing at infinity
    Yun, Yongzhen
    An, Tianqing
    Zuo, Jiabin
    Zhao, Dafang
    BOUNDARY VALUE PROBLEMS, 2019, 2019 (1) : 1 - 15
  • [37] Existence of ground state solutions for a class of Choquard equations with local nonlinear perturbation and variable potential
    Jing Zhang
    Qiongfen Zhang
    Boundary Value Problems, 2021
  • [38] Positive ground state solutions for Choquard equations with lower critical exponent and steep well potential?
    Li, Yong-Yong
    Li, Gui-Dong
    Wu, Xing-Ping
    APPLIED MATHEMATICS LETTERS, 2021, 118
  • [39] Ground state sign-changing solutions for critical Choquard equations with steep well potential
    Li, Yong -Yong
    Li, Gui-Dong
    Tang, Chun -Lei
    ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2022, (54) : 1 - 20
  • [40] Existence of ground state solutions for a class of Choquard equations with local nonlinear perturbation and variable potential
    Zhang, Jing
    Zhang, Qiongfen
    BOUNDARY VALUE PROBLEMS, 2021, 2021 (01)
12345