In this paper, we consider the following p-Laplacian equation −∆pu + |u|p−2u − λu = µ|u|q−2u + |u|p∗−2u, in RN, u > 0, ∫ RNu2dx = a2, where a,µ > 0, −∆pu = div(|∇u|p−2∇u),1 < p < N, λ ∈ R is an unknown parameter that appears as a Lagrange multiplier, p < q
