On a class of fully nonlinear elliptic equation in dimension two

Abstract

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.