Singular perturbed Kirchhoff type problem with critical exponent

In the present paper, we consider the following Kirchhoff type problem with critical exponent{−(ε2a+εb∫R3|∇u|2dx)Δu+V(x)u=f(u),inR3,u∈H1(R3). By variational methods, we show the existence of the positive solutions concentrating around global minima of the potential V(x), as ε→0. We do not need the monotonicity of the function ξ→f(ξ)ξ3.