Ground state of Kirchhoff type fractional Schrodinger equations with critical growth

被引：45
|
作者：
Zhang, Jian [1 ]
Lou, Zhenluo [2 ]
Ji, Yanju [1 ]
Shao, Wei [3 ]
机构：
[1] China Univ Petr, Coll Sci, Qingdao 266580, Shandong, Peoples R China
[2] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China
[3] QuFu Normal Univ, Sch Management, Rizhao 276826, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 462卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Fractional Schrodinger equation; Kirchhoff type; Critical growth; Variational method; SCALAR FIELD-EQUATIONS; ELLIPTIC EQUATION; EXISTENCE;
D O I：
10.1016/j.jmaa.2018.01.060
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the critical Kirchhoff type fractional Schrodinger equation: (1+alpha integral(3)(R)integral(3)(R) |u(x) - u(y)|(2)/|x-y|(3-2s) dxdy) (-Delta)(s)u + u = beta f(u) + u(2*)s 1 in R-3, (0.1) where s is an element of (0, 1) and 2(S)(*) = 6/3-2s. We establish the Pohozaev type identity of (0.1). When s is an element of[3/4, 1), under some conditions on alpha, beta and f (u), we obtain some results on the existence of ground state solutions. When s is an element of (0, 3/4], we also prove the non-existence result. In particular, when alpha = 0, we obtain an existence result. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码：57 / 83
页数：27
相关论文
共 50 条
  • [31] On ground state solutions for the Schrodinger-Poisson equations with critical growth
    Liu, Zhisu
    Guo, Shangjiang
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 412 (01) : 435 - 448
  • [32] Ground State Solutions for Generalized Quasilinear Schrodinger Equations with Critical Growth
    Li, Quanqing
    Zhang, Jian
    Nie, Jianjun
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2022, 21 (04)
  • [33] LEAST ENERGY SOLUTIONS FOR FRACTIONAL KIRCHHOFF TYPE EQUATIONS INVOLVING CRITICAL GROWTH
    Deng, Yinbin
    Huang, Wentao
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2019, 12 (07): : 1929 - 1954
  • [34] Existence of nontrivial solutions for Schrodinger-Kirchhoff type equations with critical or supercritical growth
    Li, Quanqing
    Teng, Kaimin
    Wu, Xian
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (03) : 1136 - 1144
  • [35] Existence of Ground State Sign-Changing Solutions of Fractional Kirchhoff-Type Equation with Critical Growth
    Guan, Wen
    Huo, Hai-Feng
    APPLIED MATHEMATICS AND OPTIMIZATION, 2021, 84 (SUPPL 1): : S99 - S121
  • [36] Existence of Ground State Sign-Changing Solutions of Fractional Kirchhoff-Type Equation with Critical Growth
    Wen Guan
    Hai-Feng Huo
    Applied Mathematics & Optimization, 2021, 84 : 99 - 121
  • [37] Bound states for fractional Kirchhoff equations with critical growth
    Chen, Mengyao
    Li, Qi
    COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2024,
  • [38] GROUND STATE SIGN-CHANGING SOLUTIONS FOR FRACTIONAL KIRCHHOFF TYPE EQUATIONS IN R
    Che, Guofengc
    Chen, Haibo
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2021, 11 (04): : 2017 - 2036
  • [39] Ground states for Schrodinger-Kirchhoff equations of fractional p-Laplacian involving logarithmic and critical nonlinearity
    Lv, Huilin
    Zheng, Shenzhou
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2022, 111
  • [40] Ground state solutions for the fractional Schrodinger-Poisson system with critical growth
    Peng, Qiu Ying
    Ou, Zeng-Qi
    Lv, Ying
    CHAOS SOLITONS & FRACTALS, 2021, 144
12345