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

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2016年 / 72卷 / 12期

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

页码：2865 / 2877

页数：13

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