Fractional Laplacian: Pohozaev identity and nonexistence results

In this Note we present the Pohozaev identity for the fractional Laplacian. As a consequence of this identity, we prove the nonexistence of nontrivial bounded solutions to semilinear problems with supercritical nonlinearities in star-shaped domains. (C) 2012 Published by Elsevier Masson SAS on behalf of Academie des sciences.