Multiplicity results for the Kirchhoff type equations with critical growth

被引：24
作者：
Yang, Liu [1 ]
Liu, Zhisu [2 ]
Ouyang, Zigen [2 ]
机构：
[1] Hengyang Normal Univ, Dept Math & Comp Sci, Hengyang 421008, Hunan, Peoples R China
[2] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2017年 / 63卷
关键词：
Multiplicity; Kirchhoff type equation; Critical growth; CRITICAL SOBOLEV EXPONENTS; GROUND-STATE SOLUTIONS; POSITIVE SOLUTIONS; EXISTENCE;
D O I：
10.1016/j.aml.2016.07.029
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the following Kirchhoff type equation with critical growth {-(a + b integral(Omega) vertical bar del u vertical bar(2)dx) del u = lambda u + mu vertical bar u vertical bar(2)u + vertical bar u vertical bar(4)u in Omega, u = 0 on partial derivative Omega, where a > 0, b >= 0 and Omega is a smooth bounded domain in R-3. When the real parameter mu is larger than some positive constant, we investigate the multiplicity of nontrivial solutions for the above problem with parameter lambda belonging to a left neighborhood of the Dirichlet eigenvalue of the Laplacian operator -Delta. (C) 2016 Elsevier Ltd. All rights reserved.
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页码：118 / 123
页数：6
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