Necessary and sufficient conditions on existence of radial solutions for exterior Dirichlet problem of fully nonlinear elliptic equations

TL;DR

This paper establishes the precise conditions under which radial solutions exist for a class of fully nonlinear elliptic equations in exterior domains, focusing on their behavior at infinity.

Contribution

It provides necessary and sufficient conditions for the existence of radial solutions with specified asymptotic behavior for fully nonlinear elliptic equations.

Findings

Derived exact criteria for solution existence

Characterized asymptotic behavior of solutions

Enhanced understanding of nonlinear elliptic exterior problems

Abstract

In this paper, we study the exterior Dirichlet problem for the fully nonlinear elliptic equation $f(\lambda(D^{2}u))=1$. We obtain the necessary and sufficient conditions of existence of radial solutions with prescribed asymptotic behavior at infinity.