Existence and concentration of positive solutions for a logarithmic Schrodinger equation via penalizationmethod

In this article we are concerned with the following logarithmic Schrodinger equation {-epsilon(2) Delta u + V(x)u = u log u(2,) in R-N, u is an element of H-1(R-N), where epsilon > 0, N >= 1 and V : R-N -> R is a continuous potential. Under a local assumption on the potential V, we use the variational methods to prove the existence and concentration of positive solutions for the above problem.