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Radial solvability for Pucci-Lane-Emden systems in annuli

Part of: General theory in ordinary differential equations Elliptic equations and systems Partial differential equations

Published online by Cambridge University Press:  15 March 2023

Liliane Maia Open the ORCID record for Liliane Maia [Opens in a new window] ,
Ederson Moreira dos Santos Open the ORCID record for Ederson Moreira dos Santos [Opens in a new window]  and
Gabrielle Nornberg Open the ORCID record for Gabrielle Nornberg [Opens in a new window]
Liliane Maia
Affiliation:
Departamento de Matemática, Universidade de Brasília, Brasília, Brazil ([email protected])
Ederson Moreira dos Santos
Affiliation:
Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, Brazil ([email protected])
Gabrielle Nornberg
Affiliation:
Departamento de Ingeniería Matemática, Universidad de Chile, Santiago, Chile ([email protected])
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Abstract

We establish a priori bounds, existence and qualitative behaviour of positive radial solutions in annuli for a class of nonlinear systems driven by Pucci extremal operators and Lane-Emden coupling in the superlinear regime. Our approach is purely nonvariational. It is based on the shooting method, energy functionals, spectral properties, and on a suitable criteria for locating critical points in annular domains through the moving planes method that we also prove.

Keywords

Fully nonlinear systemsradial positive solutionsannulusshooting method

MSC classification

Primary: 35J15: Second-order elliptic equations
Secondary: 35J60: Nonlinear elliptic equations 35B09: Positive solutions 34A34: Nonlinear equations and systems, general
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 154 , Issue 2 , April 2024 , pp. 494 - 507
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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