Seminario del Departamento de
Ecuaciones Diferenciales y Análisis Numérico

Fecha : 4 de junio de 2019
Hora  : 11:15
Lugar : Seminario del Departamento (Fac. de Matemáticas, 3a. planta, módulo 34)

Jaqueline Godoy Mesquita

(Universidade de Brasília, Brasília, Brasil.)

Resumen

In 1957, Jaroslav Kurzweil introduced in the literature a class of integral equations called generalized ordinary differential equations (GODEs, for short). His initial motivation was to use them to investigate results concerning contin- uous dependence of solutions with respect to parameters (see [5]). However, these equations have been shown to be a powerful tool to investigate other types of equations, such as impulsive equations, functional dynamic equations on time scales, measure functional differential equations, measure neutral functional differential equations, among others. See [1, 2, 3, 4] and the references therein. In this talk, we provide a basic overview of generalized differential equations and summarize some recent results in this area as well as we present the new trends in the study of these equations. References [1] M. Federson, M. Frasson, J. G. Mesquita, P. Tacuri, Measure Neutral Functional Differential Equations as Generalized ODEs, J. Dynamics and Differential Equations (2018) 30, 1-30. 
 [2] M. Federson; J. G. Mesquita; A. Slavík, Measure functional differential equations and functional dynamic equations on time scales, J. Differential Equations 252 (2012), 3816-3847. 
 [3] M. Federson; J. G. Mesquita; A. Slavík, Basic results for functional differential and dynamic equations involving impulses, Math. Nachr. 286(2-3) (2013), 181- 204. 
 [4] C. Gallegos, H. Henríquez, J. G. Mesquita, Measure functional differential equa- tions with infinite time-dependent delay, submitted. 
 [5] J. Kurzweil, Generalized ordinary differential equations and continuous depen- dence on a parameter, Czech. Math. J. 7(82) (1957), 418-448.