Nontrivial solutions for Kirchhoff-type problems with a parameter

被引：47
作者：
Xu, Liping [1 ]
Chen, Haibo [2 ]
机构：
[1] Henan Univ Sci & Technol, Dept Math & Stat, Luoyang 471003, Peoples R China
[2] Cent S Univ, Sch Math & Stat, Changsha 410075, Hunan, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 433卷 / 01期
关键词：
Kirchhoff-type-equations; Cerami sequence; Mountain pass theorem; Symmetric mountain pass theorem; EXISTENCE; EQUATIONS; MULTIPLICITY;
D O I：
10.1016/j.jmaa.2015.07.035
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper deals with the following Kirchhoff-type problems: { -(a + b integral N-R vertical bar del u vertical bar(2)dx)Delta u + lambda V (x)u = f (x, u) in R-N, u is an element of H-1(R-N), where constants a, b > 0, lambda >= 1 is a parameter, and f (x,u) is either sublinear or superlinear at infinity. Under relaxed assumptions on V(x), we establish the existence and multiplicity results without the compactness of embedding of the working space. (C) 2015 Elsevier Inc. All rights reserved.
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页码：455 / 472
页数：18
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