In this paper we study existence, nonexistence and classification of radial positive solutions of some weighted fully nonlinear equations involving Pucci extremal operators. Our results are entirely based on the analysis of the dynamics induced by an autonomous quadratic system which is obtained after a suitable transformation. This method allows to treat both regular and singular solutions in a unified way, without using energy arguments. In particular we recover known results on regular solutions for the fully nonlinear non weighted problem by alternative proofs. We also slightly improve the classification of the solutions for the extremal operator $\mathcal{M}^-$.

中文翻译：

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一类径向加权全非线性方程的动力学系统方法

在本文中，我们研究了一些涉及 Pucci 极值算子的加权全非线性方程的径向正解的存在、不存在和分类。我们的结果完全基于对经过适当变换后获得的自主二次系统引起的动力学的分析。这种方法允许以统一的方式处理正则解和奇异解，而无需使用能量参数。特别是，我们通过替代证明恢复了完全非线性非加权问题的常规解决方案的已知结果。我们还略微改进了极值运算符 $\mathcal{M}^-$ 的解的分类。