13-53 Alessio Fiscella, Enrico Valdinoci

A critical Kirchhoff type problem involving a non--local operator (63K, latex) Jun 11, 13

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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\|

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