Existence and concentration of positive solutions for a quasilinear equation in

We study existence and concentration of positive solutions for quasilinear elliptic equations of the form − ε 2 Δ u − ε 2 Δ ( u 2 ) u + V ( x ) u = h ( u ) in R N , N ⩾ 3 , as ε → 0 , where the potential V : R N → R has a positive infimum and inf ∂ Ω V > inf Ω V for some bounded domain Ω in R N and h is a nonlinearity without some growth conditions such as Ambrosetti–Rabinowitz.