POSITIVE SOLUTION AND GROUND STATE SOLUTION FOR A KIRCHHOFF TYPE EQUATION WITH CRITICAL GROWTH

被引：1
|
作者：
Chen, Caixia [1 ]
Qian, Aixia [2 ]
机构：
[1] Jining Univ, Math Dept, Jining 273155, Shandong, Peoples R China
[2] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China
来源：
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2022年 / 59卷 / 04期
关键词：
Kirchhoff type equation; critical nonlinearity; concentration-compactness principle; ground state solution; EXISTENCE;
D O I：
10.4134/BKMS.b210567
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider the following Kirchhoff type equation on the whole space {- (a + b integral( )(R3)vertical bar del u vertical bar(2) dx)Delta u = u(5) + lambda k(x)g(u), x is an element of R-3 u is an element of D-1,D-2(R-3), where lambda > 0 is a real number and k, g satisfy some conditions. We mainly investigate the existence of ground state solution via variational method and concentration-compactness principle.
引用
收藏
页码：961 / 977
页数：17
相关论文
共 50 条
  • [21] Ground state solution for some new Kirchhoff-type equations with Hartree-type nonlinearities and critical or supercritical growth
    Zhou, Li
    Zhu, Chuanxi
    OPEN MATHEMATICS, 2022, 20 (01): : 751 - 768
  • [22] POSITIVE SOLUTION FOR THE KIRCHHOFF-TYPE EQUATIONS INVOLVING GENERAL SUBCRITICAL GROWTH
    Liu, Jiu
    Liao, Jia-Feng
    Tang, Chun-Lei
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2016, 15 (02) : 445 - 455
  • [23] On the ground state solution for a critical fractional Laplacian equation
    Hua, Yongxia
    Yu, Xiaohui
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 87 : 116 - 125
  • [24] Ground state solutions for a quasilinear Kirchhoff type equation
    Liu, Hongliang
    Chen, Haibo
    Xiao, Qizhen
    ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2016, (90)
  • [25] The existence of a ground-state solution for a class of Kirchhoff-type equations in RN
    Liu, Jiu
    Liao, Jia-Feng
    Tang, Chun-Lei
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2016, 146 (02) : 371 - 391
  • [26] Ground state solution of the thin film epitaxy equation
    Su, Yu
    Liu, Bingyuan
    Feng, Zhaosheng
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 503 (02)
  • [27] Ground State Solution of Pohozaev Type for Quasilinear Schrodinger Equation Involving Critical Exponent in Orlicz Space
    Chen, Jianqing
    Zhang, Qian
    MATHEMATICS, 2019, 7 (09)
  • [28] Ground state of Kirchhoff type fractional Schrodinger equations with critical growth
    Zhang, Jian
    Lou, Zhenluo
    Ji, Yanju
    Shao, Wei
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 462 (01) : 57 - 83
  • [29] EXISTENCE OF SOLUTION TO CRITICAL KIRCHHOFF-TYPE EQUATION WITH DIPOLE-TYPE POTENTIAL
    Wang, Sainan
    Su, Yu
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 2022 (34) : 1 - 18
  • [30] Bounded state solution of degenerate Kirchhoff type problem with a critical exponent
    Xie, Qilin
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 479 (01) : 1 - 24
12345