Existence of solutions for Kirchhoff type problems with critical nonlinearity in R3

In this paper, we consider the existence and multiplicity of solutions of Kirchhoff type problems with critical nonlinearity in R3:−ε2(a+b∫R3|∇u|2dx)Δu+V(x)u=K(x)|u|4u+h(x,u), (t,x)∈R×R3. Under suitable assumptions, we prove that this has at least one solution and for any m∈N, it has at least m pairs of solutions.