On multiplicity and concentration of positive solutions for a class of quasilinear problems with critical exponential growth in RN

Abstract

In this work we study the existence, multiplicity and concentration of positive solutions for the following class of quasilinear problems- ε{lunate}N ΔN u + V (x) | u |N - 2 u = f (u) in RN, u (x) > 0, ∀ x ∈ RN, where ΔN u is the N-Laplacian operator, ε{lunate} is a positive parameter, N ≥ 2, V : RN → R is a continuous function and f : R → R is a C1 function having critical exponential growth. © 2008 Elsevier Inc. All rights reserved.