Existence of solutions for fourth order elliptic equations of Kirchhoff type

This paper is concerned with the existence of nontrivial solutions for a class of fourth order elliptic equations of Kirchhoff type (1){δ2u-λ(a+b∫Ω|∇;u|2dx)δu=f(x,u),inΩ,u=0,δu=0,on∂Ω, where a>0, b≥0 are constants, and λ>0 is a parameter. We will show that there exists a λ^* such that (1) has nontrivial solutions for 0<λ<λ^* by using the mountain pass techniques and the truncation method.