Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension

Zhisu Liu, Marco Squassina, Jianjun Zhang

Published 2016-12-23Version 1

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.