Generalized quasilinear asymptotically periodic Schrödinger equations with critical growth

This paper is concerned with the following quasilinear Schrödinger equations: {−div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u=λf(x,u)+g(u)|G(u)|2∗−2G(u),x∈RN,u(x)>0,x∈RN, where N≥3N≥3, 2∗=2NN−2, G(u)=∫0ug(t)dt and λ>0λ>0 is a parameter. By using a change of variable, the quasilinear equation is reduced to a semilinear one, whose associated functional is well defined in H1(RN)H1(RN). We establish the existence of positive solutions for this problem by using the Mountain Pass Theorem in combination with the concentration-compactness principle under appropriate assumptions on V(x)V(x) and f(x,u)f(x,u). Recent results from the literature are improved and extended.