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 $$ ε^{2s} (-Δ)^{s}{u}+V(z)u=f(u)\,\,\, \mbox{in} \,\,\, \mathbb{R}^{N}, $$ where $ε$ is a positive parameter, $f$ has a subcritical growth, $V$ possesses a local minimum, $N > 2s,$ $s \in (0,1),$ and $(-Δ)^{s}u$ is the fractional laplacian.

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