Generalized quasilinear Schrödinger equations with critical growth

We establish the existence of nontrivial solutions for the following quasilinear Schrödinger equation: −Δu+V(x)u−Δ[l(u2)]l′(u2)u=uα2∗−1+f(u),x∈RN,where V(x):RN→R is a given potential and l,f are real functions, 2∗=2N∕(N−2), N≥3. Our results cover two physical models l(s)=sα2, l(s)=(1+s)α2, α>1 and recent results from the literature (Shen and Wang, 2016, Deng et al., 2016) are improved and extended.