Multiplicity of concentrating solutions for a class of fractional Kirchhoff equation

被引：24
|
作者：
He, Xiaoming [1 ]
Zou, Wenming [2 ]
机构：
[1] Minzu Univ China, Coll Sci, Beijing 100081, Peoples R China
[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
来源：
MANUSCRIPTA MATHEMATICA | 2019年 / 158卷 / 1-2期
基金：
中国国家自然科学基金;
关键词：
POSITIVE SOLUTIONS; SCHRODINGER-EQUATION; CONCENTRATION BEHAVIOR; NONTRIVIAL SOLUTIONS; ELLIPTIC PROBLEMS; STANDING WAVES; GROUND-STATES; EXISTENCE; POWER;
D O I：
10.1007/s00229-018-1017-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the multiplicity of concentrating solutions to the nonlinear fractional Kirchhoff equation (e 2sa + e 4s- 3b R3 |(-) s2 u| 2dx (-) su + V( x) u = f ( u) in R-3, wheree > 0 is a positive parameter, (- s is the fractional laplacian with s. (3 4, 1), a, b are positive constants, and V is a positive potential such that inf. V > inf V for some open bounded subset . R3. We relate the number of positive solutions with the topology of the set where V attains its minimum in . The proof is based on the Ljusternik-Schnirelmann theory.
引用
收藏
页码：159 / 203
页数：45
相关论文
共 50 条
  • [1] Multiplicity of concentrating solutions for a class of fractional Kirchhoff equation
    Xiaoming He
    Wenming Zou
    manuscripta mathematica, 2019, 158 : 159 - 203
  • [2] Concentrating solutions for a fractional Kirchhoff equation with critical growth
    Ambrosio, Vincenzo
    ASYMPTOTIC ANALYSIS, 2020, 116 (3-4) : 249 - 278
  • [3] Multiplicity of nontrivial solutions for a class of fractional Kirchhoff equations
    Shao, Liuyang
    Chen, Haibo
    Pang, Yicheng
    Wang, Yingmin
    AIMS MATHEMATICS, 2024, 9 (02): : 4135 - 4160
  • [4] Multiplicity and Concentration Behavior of Solutions to a Class of Fractional Kirchhoff Equation Involving Exponential Nonlinearity
    Song, Yueqiang
    Sun, Xueqi
    Liang, Sihua
    Nguyen, Van Thin
    JOURNAL OF GEOMETRIC ANALYSIS, 2024, 34 (09)
  • [5] MULTIPLE CONCENTRATING SOLUTIONS FOR A FRACTIONAL KIRCHHOFF EQUATION WITH MAGNETIC FIELDS
    Ambrosio, Vincenzo
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (02) : 781 - 815
  • [6] Existence and Multiplicity of Solutions for Fractional κ(ξ)-Kirchhoff-Type Equation
    Sousa, J. Vanterler da C.
    Kucche, Kishor D.
    Nieto, Juan J.
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2024, 23 (01)
  • [7] Multiplicity of solutions for a fractional Kirchhoff type equation with a critical nonlocal term
    Dou, Xilin
    He, Xiaoming
    FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2023, 26 (04) : 1941 - 1963
  • [8] Multiplicity and Concentration of Solutions for a Fractional Magnetic Kirchhoff Equation with Competing Potentials
    Deng, Shengbing
    Luo, Wenshan
    ANNALES HENRI POINCARE, 2024, 25 (07): : 3499 - 3528
  • [9] MULTIPLICITY AND CONCENTRATION OF SOLUTIONS FOR A FRACTIONAL p-KIRCHHOFF TYPE EQUATION
    Chen, Wenjing
    Pan, Huayu
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2023, 43 (07) : 2576 - 2607
  • [10] Multiplicity of solutions for a fractional Kirchhoff type equation with a critical nonlocal term
    Xilin Dou
    Xiaoming He
    Fractional Calculus and Applied Analysis, 2023, 26 : 1941 - 1963
12345