Existence and concentration of solution for a class of fractional elliptic equation in ${\mathbb{R}}^N$ via penalization method

In this paper, we study the existence and concentration of positive solution for the following class of fractional elliptic equation $${ϵ}^{2s}(-\mathrm{\Delta }{)}^{s}u+V(z)u=f(u)in{\mathbb{R}}^N,$$ where $ϵ$ is a positive parameter, $f$ has a subcritical growth, $V$ possesses a local minimum, $N>2s,$ $s\in (0,1),$ and $(-\mathrm{\Delta }{)}^{s}u$ is the fractional laplacian.