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$\\alpha\\in (0,N)$, $I_\\alpha(x)={A_\\alpha\\over |x|^{N-\\alpha}}$ is the Riesz potential, $F\\in C^1(\\mathbb{R},\\mathbb{R})$, $F'(s) = f(s)$ and $\\varepsilon>0$ is a small parameter.\n  We develop a new variational approach and we show the existence of a family of solutions concentrating, as $\\varepsilon\\to 0$, to a local minima of $V(x)$ under general conditions on 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