Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument

In this paper we shall show an existence result of a positive solution for a Kirchhoff problem type in a bounded domain of R N , that is, for the problem − M ( ∫ Ω | ∇ u | 2 d x ) Δ u = λ f ( x , u ) + | u | 2 ∗ − 2 u in  Ω , u = 0 on  ∂ Ω . We shall study the asymptotic behavior of this solution when λ converges to infinity. Our approach is based on the variational method, an appropriated truncated argument, and a priori estimates to obtain the solution.