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Aim of this paper is to study the following elliptic equation driven by a general non-local integrodifferential operator    such that    in   ,    in   , where   ,    is an open bounded set of ℝ  n  ,   , with Lipschitz boundary, λ is a positive real parameter,    is a fractional critical Sobolev exponent, while    is the non-local integrodifferential operator

The Yamabe equation in a non-local setting