Existence and concentration behavior of positive solutions for a Kirchhoff equation in R3

被引：496
|
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：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2012年 / 252卷 / 02期
关键词：
Positive solutions; Kirchhoff type equation; Variational methods; NONLINEAR SCHRODINGER-EQUATIONS; QUASILINEAR ELLIPTIC-EQUATIONS; SEMICLASSICAL STATES; MULTIPLICITY; REGULARITY; PRINCIPLE;
D O I：
10.1016/j.jde.2011.08.035
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the existence, multiplicity and concentration behavior of positive solutions for the nonlinear Kirchhoff type problem {-(epsilon(2)a +epsilon b integral vertical bar del u vertical bar(2)) + V (x) u = f (u) in R-3, u is an element of H-1 (R-3), u > 0 in R-3, where epsilon > 0 is a parameter and a, b > 0 are constants: V is a positive continuous potential satisfying some conditions and f is a subcritical nonlinear term. We relate the number of solutions with the topology of the set where V attains its minimum. The results are proved by using the variational methods. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.
引用
收藏
页码：1813 / 1834
页数：22
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