On the Pohozaev identity for the fractional $p$-Laplacian operator in ${\mathbb{R}}^N$

Abstract

In this paper, we show the existence of a nontrivial weak solution for a nonlinear problem involving the fractional $p$-Laplacian operator and a Berestycki-Lions type nonlinearity. This solution satisfies a Pohozaev identity. Moreover, we prove that any sufficiently smooth solution fulfills the Pohozaev identity.

to appear in Bulletin of the London Mathematical Society