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We study a nonlinear and nonlocal elliptic equation. The problem has a variational structure, and this allows us to find a positive solution by looking at critical points of a suitable energy functional. In particular, in this paper, we find a local minimum and a mountain pass solution of this functional. One of the crucial ingredient is a Concentration-Compactness principle. Some difficulties arise from the nonlocal structure of the problem and from the fact that we deal with an equation indoi:10.34657/2382 fatcat:snt4sqeqmvcwfagohkpndekzoq