On concentration of solution to a Schrodinger logarithmic equation with deepening potential well

In this work, we prove the existence of positive solution for the following class of problems- Delta u+lambda V(x)u=ulogu(2), x is an element of R-N, u is an element of H1(R-N), where lambda>0 and V:RN -> R is a potential satisfying some conditions. Using the variational method developed by Szulkin for functionals, which are the sum of a C-1 functional with a convex lower semicontinuous functional, we prove that for each large enough lambda>0, there exists a positive solution for the problem, and that, as lambda ->+infinity, such solutions converge to a positive solution of the limit problem defined on the domain omega=int(V-1({0})).