Ground states for a fractional scalar field problem with critical growth

We prove the existence of a ground state solution for the following fractional scalar field equation $(-\mathrm{\Delta }{)}^{s}u=g(u)$ in ${\mathbb{R}}^N$ where $s\in (0,1),N>2s$,$(-\mathrm{\Delta }{)}^s$ is the fractional Laplacian, and $g\in C^{1,\beta }(\mathbb{R},\mathbb{R})$ is an odd function satisfying the critical growth assumption.