The existence of nontrivial solutions for the critical Kirchhoff type problem in RN

被引：6
|
作者：
Zhang, Jian [1 ]
Ji, Yanju [1 ]
机构：
[1] China Univ Petr, Coll Sci, Qingdao 266580, Shandong, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2017年 / 74卷 / 12期
关键词：
Kirchhoff type problem; Critical growth; Variational method; GROUND-STATE SOLUTIONS; POSITIVE SOLUTIONS; ELLIPTIC-EQUATIONS; MULTIPLICITY; EXPONENT;
D O I：
10.1016/j.camwa.2017.08.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the problem - (a + b integral(RN) vertical bar del u vertical bar(2)dx) Delta u + V(x)u = mu f(u)+ g(x)u(2)*(-1) in R-N, (0.1) where N >= 3, a, b > 0. When N = 3 and mu > 0 is small, under suitable conditions on V, f and g, we prove (0.1) has two nontrivial solutions. When N >= 4 and g(x) = 1, we also obtain the existence and non-existence results. (C) 2017 Published by Elsevier Ltd.
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页码：3080 / 3094
页数：15
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