Multiple positive solutions to a Kirchhoff type problem involving a critical nonlinearity

被引:15
作者
Zhong, Xiao-Jing [1 ,2 ]
Tang, Chun-Lei [1 ]
机构
[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China
[2] Southwest Univ, Sch Hist Culture & Ethnol, Chongqing 400715, Peoples R China
基金
中国国家自然科学基金;
关键词
Kirchhoff type problem; Nehari manifold; Critical nonlinearity; Ground state; CRITICAL SOBOLEV EXPONENTS; CHANGING WEIGHT FUNCTION; ELLIPTIC-EQUATIONS; CRITICAL GROWTH; EXISTENCE; STATES; R-3;
D O I
10.1016/j.camwa.2016.10.012
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we investigate a class of Kirchhoff type problem involving a critical nonlinearity -(1+b integral(Omega) vertical bar del u vertical bar(2)dx) Delta u = lambda u + vertical bar u vertical bar(4)u, u is an element of H-0(1)(Omega), where b > 0, lambda(1) , lambda(1) is the principal eigenvalue of (- Delta, H-0(1)(Omega). With the help of the Nehari manifold, we obtain the multiplicity of positive solutions for A in a small right neighborhood of lambda(1) and prove that one of the solutions is a positive ground state solution, which is different from the result of Brezis-Nirenberg in 1983. This paper can be regarded as the complementary work of Naimen (2015). (C) 2016 Elsevier Ltd. All rights reserved.
引用
收藏
页码:2865 / 2877
页数:13
相关论文
共 50 条
[41]   Soliton solutions to Kirchhoff type problems involving the critical growth in RN [J].
Liang, Sihua ;
Shi, Shaoyun .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 81 :31-41
[42]   p-KIRCHHOFF TYPE PROBLEM WITH A GENERAL CRITICAL NONLINEARITY [J].
Zhang, Huixing ;
Lin, Baiquan .
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2018,
[43]   Multiplicity of positive solutions for quasilinear elliptic equations involving critical nonlinearity [J].
Fang, Xiangdong ;
Zhang, Jianjun .
ADVANCES IN NONLINEAR ANALYSIS, 2020, 9 (01) :1420-1436
[44]   Multiplicity of solutions for Kirchhoff-type problems involving critical growth [J].
Zhou, Chenxing ;
Miao, Fenghua ;
Liang, Sihua ;
Song, Yueqiang .
BOUNDARY VALUE PROBLEMS, 2014, :1-14
[45]   A fractional Kirchhoff problem involving a singular term and a critical nonlinearity [J].
Fiscella, Alessio .
ADVANCES IN NONLINEAR ANALYSIS, 2019, 8 (01) :645-660
[46]   On a fractional Kirchhoff type problem with critical exponential growth nonlinearity [J].
Chen, Wenjing ;
Yu, Fang .
APPLIED MATHEMATICS LETTERS, 2020, 105
[47]   Multiple positive solutions for an elliptic problem involving a critical Sobolev exponent [J].
Zheng, Tiantian ;
Wang, Zhiyong ;
Ma, Pei ;
Zhang, Jihui .
APPLICABLE ANALYSIS, 2022, 101 (15) :5334-5357
[48]   Multiple positive solutions for a Dirichlet problem involving critical Sobolev exponent [J].
Li, Tiexiang ;
Wu, Tsung-fang .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 369 (01) :245-257
[49]   Multiple positive solutions for the critical Kirchhoff type problems involving sign-changing weight functions [J].
Xie, Weihong ;
Chen, Haibo .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 479 (01) :135-161
[50]   Multiple positive solutions for a logarithmic Kirchhoff type problem in R3 [J].
Gao, Yuan ;
Jiang, Yongsheng ;
Liu, Lishan ;
Wei, Na .
APPLIED MATHEMATICS LETTERS, 2023, 139