Multiplicity results for the Kirchhoff type equations with critical growth

In this paper, we study the following Kirchhoff type equation with critical growth {−(a+b∫Ω|∇u|2dx)△u=λu+μ|u|2u+|u|4uinΩ,u=0on∂Ω, where a>0,b≥0 and Ω is a smooth bounded domain in R3. When the real parameter μ is larger than some positive constant, we investigate the multiplicity of nontrivial solutions for the above problem with parameter λ belonging to a left neighborhood of the Dirichlet eigenvalue of the Laplacian operator −△.