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

摘要

In this work we study the existence, multiplicity and concentration of positive solutions for the following class of quasilinear problems -epsilon(N)Delta(N)u + V(X)vertical bar u vertical bar(N-2)u = f(u) in R-N, u (x) > 0. for all x is an element of R-N, where Delta(N)u is the N-Laplacian operator, epsilon is a positive parameter. N >= 2, V : R-N -> R is a continuous function and f: R -> R is a C-1 function having critical exponential growth. (C) 2008 Elsevier Inc. All rights reserved.