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In this paper we study a semilinear problem for the fractional laplacian that are the counterpart of the Neumann problems in the classical setting. We show uniqueness of minimal energy solutions for small domains. 2010 Mathematics Subject Classification. 35R11, 35J60.doi:10.1090/proc/14530 fatcat:iqv3ke4gzbh4lmldbgvwm4weqi