Large critical exponents for some second order uniformly elliptic operators

In this paper we investigate the critical exponents of two families of Pucci’s extremal operators. The notion of critical exponent that we have chosen for these fully nonlinear operators whihc are not variational is that of threshold betweeen existence and nonexistence of the solutions for semilinear equations with pure power nonlinearities. Interesting new exponents appear in this context.