Existence and concentration of positive solutions for a quasilinear equation in RN

We study existence and concentration of positive solutions for quasilinear elliptic equations of the form −ε2Δu−ε2Δ(u2)u+V(x)u=h(u) in RN, N⩾3, as ε→0, where the potential V:RN→R has a positive infimum and inf∂ΩV>infΩV for some bounded domain Ω in RN and h is a nonlinearity without some growth conditions such as Ambrosetti–Rabinowitz.