Existence of ground state solutions for a quasilinear Schrödinger equation with critical growth

We establish the existence of ground state solutions for a quasilinear Schrödinger equation −Δu+V(x)u−Δ(u2)u=∣u∣22∗−2u+λ∣u∣p−1u,inRN, where N≥3N≥3, 2∗=2NN−2, 10λ>0 is a parameter. We do not need the subcritical exponent p>3p>3 which was used by several authors to conclude the existence of solution for the equation above.