Radial solutions of Lane-Emden-Fowler equations with Pucci's extremal operators

We report on some recent results obtained for positive radial solutions of Lane-Emden-Fowler type equations with Pucci's operators as principal parts. The presented results include the asymptotic analysis of almost critical solutions in the unit ball,  existence results in annular domains and sharp Liouville-type results for exterior Dirichlet problems.