Multiple positive solutions for a Schr\"{o}dinger logarithmic equation

This article concerns with the existence of multiple positive solutions for the following logarithmic Schr"{o}dinger equation $$\{\begin{array}{lc}-{ϵ}^2\mathrm{\Delta }u+V(x)u=u\log u^2,& in{\mathbb{R}}^N,\end{array}$$ where $ϵ>0$, $N\ge 1$ and $V$ is a continuous function with a global minimum. Using variational method, we prove that for small enough $ϵ>0$, the “shape” of the graph of the function $V$ affects the number of nontrivial solutions.