Generalized linear differential equations in a Banach space: continuous dependence on parameters and applications

• Autor(a) principal: Monteiro, Giselle Antunes
• Data de Publicação: 2012
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-30032012-105214/
• topic: Dynamical equations on time scales; Equações diferenciais funcionais; Equações diferenciais generalizadas; Equações dinâmicas escalas temporais; Functional differential equations; Generalized differential equations; Integral de Kurzweil-Stieltjes; Kurzweil-Stieltjes integral

The purpose of this work is to investigate continuous dependence on parameters for generalized linear differential equations in a Banach space- valued setting. More precisely, we establish a theorem inspired by the clas- sical continuous dependence result due to Z. Opial. In addition, our second outcome extends, to Banach spaces, the result proved by M. Ashordia in the framework of finite dimensional generalized linear differential equations. Roughly speaking, the continuous dependence derives from assumptions of uniform convergence of the functions in the right-hand side of the equations, together with the uniform boundedness of variation of the linear terms. Fur- thermore, applications of these results to dynamic equations on time scales and also to functional differential equations are proposed. Besides these results on continuous dependence, we complete the theory of abstract Kurzweil-Stieltjes integration so that it is well applicable for our purposes in generalized linear differential equations. In view of this, our contributions are related not only to differential equations but also to the abstract Kurzweil-Stieltjes integration theory itself. The new results presented in this work are contained in the papers [26] and [27], both accepted for publication