  In this paper we will prove the existence of a positive solution for a class
of Schr\"odinger logarithmic equation of the form
  \begin{equation}
  \left\{\begin{aligned}
  -\Delta u &+ u =Q(x)u\log u^2,\;\;\mbox{in}\;\;\Omega,\nonumber
  &\mathcal{B}u=0 \,\,\, \mbox{on} \,\,\, \partial \Omega ,
  \end{aligned}
  \right.
  \end{equation}
  where $\Omega \subset \mathbb{R}^N$, $N \geq 3$, is an \textit{exterior
domain}, i.e., $\Omega^c=\mathbb{R}^N \setminus \Omega$ is a bounded smooth
domain where $\mathcal{B}u=u$ or $\mathcal{B}u=\frac{\partial u}{\partial
\nu}$. 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.
