A class of quasilinear Schrödinger equations with critical or supercritical exponents

We study the existence of nontrivial solutions for the following quasilinear Schrödinger equations −Δu+V(x)u+κ2[Δ∣u∣2]u=l(u),x∈RN, where V:RN→R and l(u) involves critical or supercritical exponents.