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We consider the nonlinear fractional problem  \begin{align*}  (-\Delta)^{s} u + V(x) u = f(x,u) &\quad \hbox{in $\mathbb{R}^N$}\end{align*} We show that ground state solutions converge (along a subsequence)in $L^2_{\mathrm{loc}} (\mathbb{R}^N)$, under suitable conditions on $f$ and$V$, to a weak solution of the local problem as $s \to 1^-$.

Non-local to local transition for ground states of fractional Schr\"{o}dinger equations on $\mathbb{R}^N$