We study existence, nonexistence, and uniqueness of positive radial solutions for a class of nonlinear systems driven by Pucci extremal operators under a Lane-Emden coupling configuration. Our results are based on the analysis of the associated quadratic dynamical system and energy methods. For both regular and exterior domain radial solutions we obtain new regions of existence and nonexistence. Besides, we show an exclusion principle for regular solutions, either in RN or in a ball, by exploiting the uniqueness of trajectories produced by the flow. In particular, for the standard Lane-Emden system involving the Laplacian operator, we prove that the critical hyperbola of regular radial positive solutions is also the threshold for existence and nonexistence of radial exterior domain solutions with Neumann boundary condition. As a byproduct, singular solutions with fast decay at infinity are also found.

Existence, nonexistence and uniqueness for Lane–Emden type fully nonlinear systems / Maia, Liliane; Nornberg, Gabrielle; Pacella, Filomena. - In: NONLINEARITY. - ISSN 0951-7715. - 36:3(2023), pp. 1510-1546. [10.1088/1361-6544/acb399]

Existence, nonexistence and uniqueness for Lane–Emden type fully nonlinear systems

Pacella, Filomena
2023

Abstract

We study existence, nonexistence, and uniqueness of positive radial solutions for a class of nonlinear systems driven by Pucci extremal operators under a Lane-Emden coupling configuration. Our results are based on the analysis of the associated quadratic dynamical system and energy methods. For both regular and exterior domain radial solutions we obtain new regions of existence and nonexistence. Besides, we show an exclusion principle for regular solutions, either in RN or in a ball, by exploiting the uniqueness of trajectories produced by the flow. In particular, for the standard Lane-Emden system involving the Laplacian operator, we prove that the critical hyperbola of regular radial positive solutions is also the threshold for existence and nonexistence of radial exterior domain solutions with Neumann boundary condition. As a byproduct, singular solutions with fast decay at infinity are also found.
2023
fully nonlinear systems; Liouville properties; existence of positive solution; uniqueness; dynamical system
01 Pubblicazione su rivista::01a Articolo in rivista
Existence, nonexistence and uniqueness for Lane–Emden type fully nonlinear systems / Maia, Liliane; Nornberg, Gabrielle; Pacella, Filomena. - In: NONLINEARITY. - ISSN 0951-7715. - 36:3(2023), pp. 1510-1546. [10.1088/1361-6544/acb399]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1721539
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