Existence and multiplicity of solutions for fourth-order elliptic equations of Kirchhoff type via genus theory

Boundary value problems

Liping Xu¹  Haibo Chen³ 

[1] Department of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, People’School of Mathematics and Statistics, Central South University, Changsha, People’s Republic of China

关键词: fourth-order elliptic equations of Kirchhoff type;    genus theory;    variational methods;   

DOI  :  10.1186/s13661-014-0212-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we study the following fourth-order elliptic equations of Kirchhoff type:△2u−(a+b∫R3|∇u|2dx)△u+V(x)u=f(x,u), inR3,u∈H2(R3), wherea,b>0are constants, we have the potentialV(x):R3→Rand the nonlinearityf(x,u):R3×R→R. Under certain assumptions onV(x)andf(x,u), we show the existence and multiplicity of negative energy solutions for the above system based on the genus properties in critical point theory. MSC: 35J20, 35J65, 35J60.

【 授权许可】

CC BY