On a class of fully nonlinear elliptic equation in dimension two

We study existence and asymptotic behavior of radial positive solutions of some fully nonlinear equations involving Pucci's extremal operators in dimension two. In particular we prove the existence of a positive solution of a fully nonlinear version of the Liouville equation in the plane. Moreover for the $\mathcal{M}^-_{\lambda,\Lambda}$ operator, we show the existence of a critical exponent and give bounds for it.