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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.
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页码:2865 / 2877
页数:13
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