Raffaella Servadei and Enrico Valdinoci
Fractional Laplacian equations with critical Sobolev exponent
(65K, LaTeX)

ABSTRACT.  In this paper we complete the study of the following elliptic equation driven by a general non-local integrodifferential operator~$\mathcal L_K$ 
$$\left\{ 
egin{array}{ll} 
\mathcal L_K u+\lambda u+|u|^{2^*-2}u+f(x, u)=0 & \mbox{in } \Omega\ 
u=0 & \mbox{in } \RR^n\setminus \Omega\,. 
\end{array}
ight.$$