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 ${\mathcal{M}}_{\lambda ,\mathrm{\Lambda }}^{-}$ operator, we show the existence of a critical exponent and give bounds for it.

中文翻译：

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一类全非线性二维椭圆方程

我们研究了一些完全非线性方程的径向正解的存在性和渐近行为，这些方程涉及二维的 Pucci 极值算子。特别地，我们证明了平面中刘维尔方程的完全非线性版本的正解的存在。此外对于${\mathcal{米}}_{\lambda ,\mathrm{\Lambda }}^{-}$ 运算符，我们证明了临界指数的存在并给出了它的界限。