Classification of radial solutions for fully nonlinear equations with Hardy potential

Liliane Maia; Gabrielle Nornberg; Filomena Pacella

doi:10.3934/dcds.2024025

Article Contents

2024, Volume 44, Issue 8: 2232-2251. Doi: 10.3934/dcds.2024025

This issue Previous Article New results on controllability and stability for degenerate Euler-Bernoulli type equations Next Article Closest distance between iterates of typical points

Classification of radial solutions for fully nonlinear equations with Hardy potential

1.
Universidade de Brasília, Brazil
2.
Universidad de Chile, Chile
3.
Sapienza Università di Roma, Italy

^*Corresponding author: Liliane Maia
^*Corresponding author: Liliane Maia

Received: October 2023

Early access: March 12, 2024

Published online: March 12, 2024

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Abstract

We study existence, nonexistence and regularity of positive radial solutions for a class of nonlinear equations driven by Pucci extremal operators, power nonlinearity and Hardy weight. We classify both regular continuous nondifferentiable and singular solutions defined in radial domains, punctured or not. We also obtain critical threshold exponents for the solvability in the exterior of a ball, as well as uniqueness and symmetry in annuli. Our results are based on the behavior of the trajectories described through suitable dynamical systems on the plane, in addition to energy monotonicity and asymptotic analysis.

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Mathematics Subject Classification: Primary: 35J15, 35J60; Secondary: 35B09, 34A34.

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Figure 1. The flow when $ a\in (-2,-1) $ and $ p\in (0,1) $.

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Figure 2. The case $ a = -2 $ in the sublinear and superlinear scenarios.

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