Singular perturbed Kirchhoff type problem with critical exponent

被引：10
作者：
Xie, Qilin [1 ]
机构：
[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 454卷 / 01期
基金：
中国博士后科学基金;
关键词：
Kirchhoff type problem; Critical exponent; Concentration behavior; NONLINEAR SCHRODINGER-EQUATIONS; POSITIVE SOLUTIONS; STANDING WAVES; NONTRIVIAL SOLUTIONS; STATE SOLUTIONS; GROUND-STATES; BOUND-STATES; EXISTENCE; MULTIPLICITY; R-3;
D O I：
10.1016/j.jmaa.2017.04.048
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present paper, we consider the following Kirchhoff type problem with critical exponent (-(epsilon(2)a + epsilon b integral(R3)vertical bar del u vertical bar(2)dx)Delta u + V(x)u = f(u), in R-3 u is an element of H-1(R-3). By variational methods, we show the existence of the positive solutions concentrating around global minima of the potential V(x), as epsilon -> 0. We do not need the monotonicity of the function xi -> f(xi)/xi(3). (C) 2017 Elsevier Inc. All rights reserved.
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收藏
页码：144 / 180
页数：37
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