Alessio Fiscella, Enrico Valdinoci
A critical Kirchhoff type problem involving a non--local operator
(63K, latex)

ABSTRACT.  In this paper we show the existence of non-negative 
solutions for a Kirchhoff type problem driven by a non--local 
integrodifferential operator, that is $$ 
-M(\left\|u
ight\|^{2}_{Z})\mathcal L_Ku=\lambda 
f(x,u)+\left|u
ight|^{2^* -2}u\quad \mbox{in }\,\,\Omega,\qquad 
u=0\quad\mbox{in}\,\,\mathbb{R}^{n}\setminus\Omega. $$ where $\mathcal 
L_K$ is an integrodifferential operator with kernel~$K$, $\Omega$ is a 
bounded subset of $\mathbb{R}^n$, $M$ and $f$ are continuous functions, 
$\left\|