# Liouville-type results in exterior domains for radial solutions of fully nonlinear equations

## TL;DR

This paper establishes precise conditions under which positive radial solutions exist for a class of fully nonlinear elliptic equations outside a ball in Euclidean space, advancing understanding of boundary value problems in exterior domains.

## Contribution

It provides necessary and sufficient criteria for positive radial solutions of fully nonlinear elliptic equations in exterior domains with Dirichlet boundary conditions.

## Key findings

- Derived exact existence conditions for solutions
- Characterized solution behavior in exterior domains
- Enhanced understanding of nonlinear elliptic boundary problems

## Abstract

We give necessary and sufficient conditions for the existence of positive radial solutions for a class of fully nonlinear uniformly elliptic equations posed in the complement of a ball in $\mathbb R^N$, and equipped with homogeneous Dirichlet boundary conditions.