Ground states for fractional Kirchhoff equations with critical   nonlinearity in low dimension
  We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential $V$. Under suitable assumptions on $V$, using the monotonicity trick and the profile decomposition, we prove the existence of ground states. In particular, the nonlinearity does not satisfy the Ambrosetti-Rabinowitz type condition or monotonicity assumptions. 
Zhisu Liu, Marco Squassina, Jianjun Zhang
math.AP