MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE

In this paper, we concern with the following fourth order elliptic equations of Kirchhoff type {Δ^2u-（a＋bfR^3｜↓△u｜^2dx）△u＋V（x）u=f（x,u）,x∈R^3, u∈H^2（R3）,where a, b 〉 0 are constants and the primitive of the nonlinearity f is of superlinear growth near infinity in u and is also allowed to be sign-chan...

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Bibliographic Details
Published inActa mathematica scientia Vol. 35; no. 5; pp. 1067 - 1076
Main Author 许丽萍 陈海波
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.09.2015
Department of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China%School of Mathematics and Statistics, Central South University, Changsha 410075, China
Subjects
35J20
35J60
35J65
fourth order elliptic equations of Kirchhoff type
symmetric mountain pass theorem
variational methods
变分方法
四阶椭圆型方程
基尔霍夫
多解性
多重性
解的存在性
超线性
非线性项
symmetric mountain pass theorem
variational methods
35J65
35J20
35J60
fourth order elliptic equations of Kirchhoff type
Online AccessGet full text
ISSN0252-9602
1572-9087
DOI10.1016/S0252-9602(15)30040-0

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Summary:In this paper, we concern with the following fourth order elliptic equations of Kirchhoff type {Δ^2u-（a＋bfR^3｜↓△u｜^2dx）△u＋V（x）u=f（x,u）,x∈R^3, u∈H^2（R3）,where a, b 〉 0 are constants and the primitive of the nonlinearity f is of superlinear growth near infinity in u and is also allowed to be sign-changing. By using variational methods, we establish the existence and multiplicity of solutions. Our conditions weaken the Ambrosetti- Rabinowitz type condition.
Bibliography:fourth order elliptic equations of Kirchhoff type; symmetric mountain pass theorem; variational methods
42-1227/O
In this paper, we concern with the following fourth order elliptic equations of Kirchhoff type {Δ^2u-（a＋bfR^3｜↓△u｜^2dx）△u＋V（x）u=f（x,u）,x∈R^3, u∈H^2（R3）,where a, b 〉 0 are constants and the primitive of the nonlinearity f is of superlinear growth near infinity in u and is also allowed to be sign-changing. By using variational methods, we establish the existence and multiplicity of solutions. Our conditions weaken the Ambrosetti- Rabinowitz type condition.
Liping XU, Haibo CHEN（1.Department of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China;2. School of Mathematics and Statistics, Central South University, Changsha 410075, China）
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(15)30040-0