New existence and multiplicity of nontrivial solutions for nonlocal elliptic Kirchhoff type problems

被引：91
作者：
Cheng, Bitao [1 ]
机构：
[1] Qujing Normal Univ, Coll Math & Informat Sci, Qujing 655011, Yunnan, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 394卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Mountain pass theorem; Kirchhoff type problems; Multiple solutions; Cut-off technique; SIGN-CHANGING SOLUTIONS; POSITIVE SOLUTIONS; EQUATION;
D O I：
10.1016/j.jmaa.2012.04.025
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present paper, we study the existence and multiplicity of nontrivial solutions for nonlocal elliptic Kirchhoff type problems {- (a + b integral(Omega) vertical bar del u vertical bar(2) dx) Delta u = f(x, u), in Omega; u = 0, on delta Omega, where a, b > 0 are real numbers. Some new existence and multiplicity results of nontrivial solutions are obtained by means of the mountain pass theorem and a cut-off technique. One known result is improved. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：488 / 495
页数：8
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