Bound state solutions of Kirchhoff type problems with critical exponent

In the present paper, we consider the following Kirchhoff type problems{−(a+b∫R3|∇u|2dx)Δu+V(x)u=u5,inR3,u∈D1,2(R3), where a>0,b>0a>0,b>0 and V∈L32(R3) is a given nonnegative function. If |V|32 is suitable small, we prove that this problem has at least one bound state solution.