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

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−

On unique continuation principles for some elliptic systems

In this paper we prove unique continuation principles for some systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application, we obtain nonexistence of nontrivial (not necessarily positive) radial solutions for the Lane-Emden system posed in a ball, in the critical and supercritical regimes. Some of our results also apply to general fully nonlinear operators, such as Pucci's extremal operators, being new even for scalar equations.Comment: 18 page

Radial solutions for Hénon type fully nonlinear equations in annuli and exterior domains

In this note we study existence of positive radial solutions in annuli and exterior domains for a class of nonlinear equations driven by Pucci extremal operators subject to a Hénon type weight. Our approach is based on the shooting method applied to the corresponding ODE problem, energy arguments, and the associated flow of an autonomous quadratic dynamical system

Uma hierarquia de testes de convergência de séries baseada no teorema de Kummer

In this study we use Kummer’s theorem on convergence of numericalpositive series in order to construct a hierarchy of specific tests, starting from the well-known simple criteria with a less range of application, and reaching more sophisticated results with a wider abrangency. We construct various examples, which illustrate the use of such tests, and analyze situations when all the tests of the presented hierarchy are not conclusive with respect to behavior of a series