Polynomial first integrals for weight-homogeneous planar polynomial differential systems of weight degree 4

Altres ajuts: ICREA AcademiaWe classify all of the weight-homogeneous planar polynomial differential systems of weight degree 4 having a polynomial first integral

Centers of discontinuous piecewise smooth quasi-homogeneous polynomial differential systems

In this paper we investigate the center problem for the discontinuous piecewise smooth quasi-homogeneous but non-homogeneous polynomial differential systems. First, we provide sufficient and necessary conditions for the existence of a center in the discontinuous piecewise smooth quasi-homogeneous polynomial differential systems. Moreover, these centers are global, and the period function of their periodic orbits is monotonic. Second, we characterize the centers of the discontinuous piecewise smooth quasi-homogeneous cubic and quartic polynomial differential systems

Cyclicity of a simple focus via the vanishing multiplicity of inverse integrating factors

First we provide new properties about the vanishing multiplicity of the inverse integrating factor of a planar analytic differential system at a focus. After we use this vanishing multiplicity for studying the cyclicity of some simple foci of several classes of planar analytic differential systems

18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems: Proceedings

Proceedings of the 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems, which took place in Dresden, Germany, 26 – 28 May 2010.:Welcome Address ........................ Page I Table of Contents ........................ Page III Symposium Committees .............. Page IV Special Thanks ............................. Page V Conference program (incl. page numbers of papers) ................... Page VI Conference papers Invited talks ................................ Page 1 Regular Papers ........................... Page 14 Wednesday, May 26th, 2010 ......... Page 15 Thursday, May 27th, 2010 .......... Page 110 Friday, May 28th, 2010 ............... Page 210 Author index ............................... Page XII

Sistemas de equações diferenciais não lineares de ordem superior em domínios limitados ou não limitados

The Boundary value problems on bounded or unbounded intervals, involving two or more coupled systems of the nonlinear differen- tial equations with full nonlinearities are scarce and have gap in literature. The present work modestly try to fill this gap. The systems covered in the work are essentially of the second- order (except for the first chapter of the first part) with boundary constraints either in bounded or unbounded intervals presented in several forms and conditions (three points, mixed, with functional dependence, homoclinic and heteroclinic). The existence, and in some cases, the localization of the solu- tions is carried out in of Banach space and norms considered, fo- llowing arguments and approaches such as: Schauder’s fixed-point theorem or of Guo–Krasnosel’ski˘ı fixed-point theorem in cones, allied to Green’s function or its estimates, lower and upper solutions, convenient truncatures, the Nagumo condition presented in different forms, concept of equiconvergence, Carathéodory functions and sequences. On the other hand, parallel to the theoretical explanation of this work, there is a range of practical examples and applications involving real phenomena, focusing on the physics, mechanics, bio- logy, forestry, and dynamical systems; A falta ou a raridade de problemas de valor fronteira na literatura, quer em dom´ınios limitados ou ilimitados, envolvendo sistemas de duas ou mais equações n˜ao lineares acopladas com todas as n˜ao linearidades completas, levou à elaboração do presente trabalho. Os sistemas abordados no trabalho s˜ao essencialmente de segunda ordem (exceto o primeiro capítulo da primeira parte) com condições de fronteira em domínios limitados ou ilimitados, de diversos tipos (três pontos, mistas, com condições funcionais, homoclínicas e heteroclínicas). A existência e em alguns casos a localização das soluções dos sistemas è considerada em espaços de Banach, seguindo vários ar- gumentos e abordagens: o teorema de ponto fixo de Schauder ou de Guo–Krasnosel’ski˘ı em cones, aliados a funções de Green ou suas estimativas, sub e sobre-soluções, truncaturas convenientes, a condição de Nagumo apresentada sob várias formas, o conceito de equiconvergência e funções e sucess˜oes de Carath´eodory. Por outro lado, paralelamente àcomponente teórica do trabalho, encontra-se um leque de aplicações e exemplos práticos envolvendo fenómenos reais, com enfoque na física, mecânica, biologia, exploração florestal e sistemas dinâmico