  In this paper we study ground states of the following fractional
Schr\"odinger equation
  (- \Delta)^{s} u + V(x) u = f(x, u) \, \mbox{ in } \, \R^{N},
  u\in \H^{s}(\R^{N})
  where $s\in (0,1)$, $N>2s$ and $f$ is a continuous function satisfying a
suitable growth assumption weaker than the Ambrosetti-Rabinowitz condition. We
consider the cases when the potential $V(x)$ is $1$-periodic or has a bounded
potential well.
