Multiple Sign-Changing Solutions for Kirchhoff-Type Equations

被引：1
|
作者：
Li, Xingping [1 ,2 ]
He, Xiumei [3 ]
机构：
[1] Yunnan Univ, Dept Math & Stat, Kunming 650091, Yunnan, Peoples R China
[2] Yunnan Normal Univ, Dept Math, Kunming 650092, Yunnan, Peoples R China
[3] Kunming Univ, Dept Math, Kunming 650214, Yunnan, Peoples R China
来源：
DISCRETE DYNAMICS IN NATURE AND SOCIETY | 2015年 / 2015卷
关键词：
HIGH-ENERGY SOLUTIONS; R-N; NONTRIVIAL SOLUTIONS; EXISTENCE;
D O I：
10.1155/2015/985986
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the following Kirchhoff-type equations -(a + b integral(Omega)vertical bar del u vertical bar(2))Delta u + V(x)u = f(x, u), in Omega, u = 0, in partial derivative Omega, where Omega is a bounded smooth domain of R-N (N = 1, 2, 3), a > 0,b >= 0, f is an element of C((Omega) over bar x R, R), and V is an element of C((Omega) over bar, R). Under some suitable conditions, we prove that the equation has three solutions of mountain pass type: one positive, one negative, and sign-changing. Furthermore, if f is odd with respect to its second variable, this problem has infinitely many sign-changing solutions.
引用
收藏
页数：9
相关论文
共 50 条
  • [41] Existence and concentration of sign-changing solutions to Kirchhoff-type system with Hartree-type nonlinearity
    Li, Fuyi
    Gao, Chunjuan
    Zhu, Xiaoli
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 448 (01) : 60 - 80
  • [42] Sign-changing solutions for Kirchhoff-type variable-order fractional Laplacian problems
    Jianwen Zhou
    Yueting Yang
    Wenbo Wang
    [J]. Boundary Value Problems, 2024
  • [43] Sign-changing solutions for Kirchhoff-type variable-order fractional Laplacian problems
    Zhou, Jianwen
    Yang, Yueting
    Wang, Wenbo
    [J]. BOUNDARY VALUE PROBLEMS, 2024, 2024 (01)
  • [44] EXISTENCE AND CONCENTRATION OF LEAST ENERGY SIGN-CHANGING SOLUTIONS FOR CRITICAL KIRCHHOFF-TYPE EQUATIONS WITH A STEEP POTENTIAL WELL
    Tian, Qin-Lin
    Tang, Chun-Lei
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2024,
  • [45] Existence of multiple solutions of Kirchhoff type equation with sign-changing potential
    Zhang, Jian
    Tang, Xianhua
    Zhang, Wen
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 242 : 491 - 499
  • [46] 3 Existence of sign-changing solution with least energy for a class of Kirchhoff-type equations in RN
    Yao, Xianzhong
    Mu, Chunlai
    [J]. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2017, (32) : 1 - 14
  • [47] EXISTENCE OF RADIAL SIGN-CHANGING SOLUTIONS FOR FRACTIONAL KIRCHHOFF-TYPE PROBLEMS IN R3
    Zhou, Mengyun
    Lan, Yongyi
    [J]. JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS, 2023, 7 (02): : 223 - 234
  • [48] Existence and asymptotic behavior of sign-changing solutions for fractional Kirchhoff-type problems in low dimensions
    Chen, Sitong
    Tang, Xianhua
    Liao, Fangfang
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2018, 25 (05):
  • [49] Existence of Ground State Sign-Changing Solutions of Fractional Kirchhoff-Type Equation with Critical Growth
    Wen Guan
    Hai-Feng Huo
    [J]. Applied Mathematics & Optimization, 2021, 84 : 99 - 121
  • [50] GROUND STATE SIGN-CHANGING SOLUTIONS FOR FRACTIONAL KIRCHHOFF TYPE EQUATIONS IN R
    Che, Guofengc
    Chen, Haibo
    [J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2021, 11 (04): : 2017 - 2036
12345