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

被引：0
作者：
Liping Xu
Haibo Chen
机构：
[1] Henan University of Science and Technology,Department of Mathematics and Statistics
[2] Central South University,School of Mathematics and Statistics
来源：
Boundary Value Problems | / 2014卷
关键词：
fourth-order elliptic equations of Kirchhoff type; genus theory; variational methods;
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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), in R3, u∈H2(R3), where a,b>0 are constants, we have the potential V(x):R3→R and the nonlinearity f(x,u):R3×R→R. Under certain assumptions on V(x) and f(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.
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