Radial solutions for H\'enon type fully nonlinear equations in annuli and exterior domains

TL;DR

This paper investigates the existence of positive radial solutions for nonlinear equations involving Pucci extremal operators with Hénon type weights in annuli and exterior domains, using shooting methods and dynamical systems analysis.

Contribution

It introduces a novel approach combining shooting methods, energy arguments, and dynamical systems to establish existence results for fully nonlinear Hénon type equations.

Findings

Positive radial solutions exist under certain conditions.

The method applies to a class of fully nonlinear equations.

Results extend previous work on Hénon type problems.

Abstract

In this note we study existence of positive radial solutions in annuli and exterior domains for a class of nonlinear equations driven by Pucci extremal operators subject to a H\'enon type weight. Our approach is based on the shooting method applied to the corresponding ODE problem, energy arguments, and the associated flow of an autonomous quadratic dynamical system.