Existence of a positive solution for a class of Schrödinger logarithmic equations on exterior domains

In this paper we will prove the existence of a positive solution for a class of Schrödinger logarithmic equation of the form. - Δ u + u = Q ( x ) u log u 2 , in Ω , B u = 0 on ∂ Ω , where Ω ⊂ R N , N ≥ 3 , is an exterior domain , i.e., Ω c = R N \ Ω is a bounded smooth domain where B u = u or B u = ∂ u ∂ ν . We have used new approach that allows us to apply the usual C 1 -variational methods to get a nontrivial solutions for these classes of problems.