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 (−∆u + λV (x)u = ulogu2, x ∈RN, u ∈ H1(RN), where λ > 0 and V : RN →R is a potential satisfying some conditions. Using the variational method developed by Szulkin for functionals which are sum of a C1 functional with a convex lower semicontinuous functional, we prove that for each λ > 0 large enough there exists a positive solutions and, as λ → +∞, such solutions converge to a positive solution of the limit problem in Ω = int(V−1({0})).