Ground states for superlinear fractional Schr\"odinger equations in   \R^{N}
  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. 
Vincenzo Ambrosio
math.AP