Multiplicity of concentrating solutions for a class of fractional Kirchhoff equation

被引：25

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

页码：159 / 203

页数：45

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