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

Abstract

We study existence and concentration of positive solutions for quasilinear elliptic equations of the form -ε2Δ;u-ε2Δ;(u2)u+V(x)u=h(u) in RN, N ≥ 3, as .ε → O, where the potential V:RN → R has a positive infimum and inf∂ Ω V > inf Ω V for some bounded domain Ω in RN and h is a nonlinearity without some growth conditions such as Ambrosetti-Rabinowitz. © 2010 Elsevier Inc.