New concentration phenomena for a class of radial fully nonlinear equations

TL;DR

This paper investigates the existence, asymptotic behavior, and concentration phenomena of sign-changing radial solutions to fully nonlinear elliptic equations involving Pucci's operators, identifying a new critical exponent and analyzing energy limits.

Contribution

It introduces a new critical exponent for these equations and describes novel concentration phenomena as parameters approach critical values.

Findings

Identified a new critical exponent for solution existence.

Described asymptotic concentration phenomena near critical exponents.

Computed the limit of a weighted energy for solutions.

Abstract

We study radial sign-changing solutions of a class of fully nonlinear elliptic Dirichlet problems in a ball, driven by the extremal Pucci's operators and with a power nonlinear term. We first determine a new critical exponent related to the existence or nonexistence of such solutions. Then we analyze the asymptotic behavior of the radial nodal solutions as the exponents approach the critical values, showing that new concentration phenomena occur. Finally we define a suitable weighted energy for these solutions and compute its limit value.