Abstract. In this paper we study existence, nonexistence and classification of radial positive solutions of some weighted fully nonlinear equations involving Pucci extremal operators. Our results are entirely based on the analysis of the dynamics induced by an autonomous quadratic system which is obtained after a suitable transformation. This method allows to treat both regular and singular solutions in a unified way, without using energy arguments. In particular we recover known results on regular solutions for the fully nonlinear non weighted problem by alternative proofs. We also slightly improve the classification of the solutions for the extremal operator M−.

A dynamical system approach to a class of radial weighted fully nonlinear equations / Pacella, Filomena; Maia, Liliane; Nornberg, Gabrielle. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - (2021).

A dynamical system approach to a class of radial weighted fully nonlinear equations

Filomena Pacella;
2021

Abstract

Abstract. In this paper we study existence, nonexistence and classification of radial positive solutions of some weighted fully nonlinear equations involving Pucci extremal operators. Our results are entirely based on the analysis of the dynamics induced by an autonomous quadratic system which is obtained after a suitable transformation. This method allows to treat both regular and singular solutions in a unified way, without using energy arguments. In particular we recover known results on regular solutions for the fully nonlinear non weighted problem by alternative proofs. We also slightly improve the classification of the solutions for the extremal operator M−.
2021
Fully nonlinear equations; critical exponent; radial solutions
01 Pubblicazione su rivista::01a Articolo in rivista
A dynamical system approach to a class of radial weighted fully nonlinear equations / Pacella, Filomena; Maia, Liliane; Nornberg, Gabrielle. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - (2021).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1469127
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