A critical Kirchhoff type problem involving a nonlocal operator

In this paper we show the existence of non-negative solutions for a Kirchhoff type problem driven by a nonlocal integrodifferential operator, that is −M(‖u‖Z2)LKu=λf(x,u)+|u|2∗−2uin  Ω,u=0in  Rn∖Ω where LKLK is an integrodifferential operator with kernel  KK, ΩΩ is a bounded subset of RnRn, MM and ff are continuous functions, ‖⋅‖Z‖⋅‖Z is a functional norm and 2∗2∗ is a fractional Sobolev exponent.