论文标题
用于一类径向加权的完全非线性方程的动态系统方法
A dynamical system approach to a class of radial weighted fully nonlinear equations
论文作者
论文摘要
在本文中，我们研究了涉及Pucci极端运算符的某些加权完全非线性方程的径向阳性溶液的存在，不存在和分类。我们的结果完全基于对合适转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常规和单数解决方案，而无需使用能量论点。特别是，我们通过替代证明对全线非加权问题的常规解决方案恢复已知结果。我们还稍微改善了极端操作员$ \ MATHCAL {M}^ - $的解决方案的分类。
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 $\mathcal{M}^-$.
