  This paper is devoted to the proof of the existence of the principal
eigenvalue and related eigenfunctions for fully nonlinear uniformly elliptic
equations posed in a punctured ball, in presence of a singular potential. More
precisely, we analyze existence, uniqueness and regularity of solutions $(
\bar\lambda_\gamma, u_\gamma)$ of the equation $$F( D^2 u_\gamma)+ \bar
\lambda_\gamma \frac{u_\gamma}{r^\gamma} = 0\ {\rm in} \ B(0,1)\setminus \{0\},
\ u_\gamma = 0 \ {\rm on} \ \partial B(0,1)$$
  where $u_\gamma>0$ in $B(0,1)\setminus \{0\}$, and $\gamma >0$. We prove
existence of radial solutions which are continuous on $\overline{ B(0,1)}$ in
the case $\gamma <2$, existence of unbounded solutions in the case $\gamma = 2$
and a non existence result for $\gamma >2$.
  We also give the explicit value of $\bar \lambda_2$ in the case of Pucci's
operators, which generalizes the Hardy--Sobolev constant for the Laplacian.
