A dynamical system approach to a class of radial weighted fully nonlinear equations

TL;DR

This paper uses a dynamical systems approach to analyze radial solutions of weighted fully nonlinear equations involving Pucci operators, providing new insights and alternative proofs for existing results.

Contribution

It introduces a dynamical system method to study solutions of weighted nonlinear equations, unifying regular and singular cases without energy methods.

Findings

Classifies radial solutions for weighted fully nonlinear equations.

Provides alternative proofs for known results on regular solutions.

Improves the classification of solutions for the extremal operator .

Abstract

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 $\mathcal{M}^-$.