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
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