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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.