Radial singular solutions of fully nonlinear equations in punctured balls

TL;DR

This paper classifies the asymptotic behavior of all radial solutions to certain fully nonlinear elliptic equations with singular and superlinear terms in punctured balls, revealing their singular nature at the origin.

Contribution

It provides a complete classification of the asymptotic behavior of radial solutions near the singularity for a class of fully nonlinear elliptic equations with inverse quadratic potential.

Findings

All radial solutions are singular at the origin.

The asymptotic behavior depends on the exponent p.

A comprehensive classification of solutions' behavior near the singularity.

Abstract

We study fully nonlinear uniformly elliptic equations having a singular reaction term with inverse quadratic potential and an absorbing superlinear term of p-power type. We consider equations posed in punctured balls centered at the origin, and we prove that all radial solutions are singular around the origin, by providing a complete classification in dependence of p of their asymptotic behavior near the singularity.