Multiplicity of nontrivial solutions for a critical degenerate Kirchhoff type problem

In this paper, we study the following Kirchhoff type problem with critical growth −M∫Ω|∇u|2dx△u=λ|u|2u+|u|4uinΩ,u=0on ∂Ω,where Ω is a smooth bounded domain in R3, M∈C(R+,R) and λ>0. We prove the existence of multiple nontrivial solutions for the above problem, when parameter λ belongs to some left neighborhood of the eigenvalue of the nonlinear operator −M(∫Ω|∇u|2dx)△.