On ground states for the Kirchhoff-type problem with a general critical nonlinearity

被引：54

作者：

Liu, Zhisu ^{[1
]}

Guo, Shangjiang ^{[1
]}

机构：

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 426卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Kirchhoff type problem; Critical nonlinearity; Ground state; Variational methods; SCALAR FIELD-EQUATIONS; POSITIVE SOLUTIONS; NONTRIVIAL SOLUTIONS; EXISTENCE; MULTIPLICITY;

D O I：

10.1016/j.jmaa.2015.01.044

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the following Kirchhoff-type problem {-(a + b integral(R3) vertical bar del u vertical bar(2)) Delta u = f(u), in R-3, u is an element of H-1 (R-3), u > 0, in R-3, where a, b > 0 are constants, and f has a critical growth. The aim of this paper is to study the existence of ground state solutions for Kirchhoff-type equations with a general nonlinearity in the critical growth, without the assumption of the monotonicity of the function t -> f(t)/t(3). Moreover, we will show that the mountain pass value gives the least energy level and also obtain a mountain pass solution. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：267 / 287

页数：21

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