Generalized ordinary differential equations and applications to classical differential equations

Author(s)

Eduard Toon

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2012-08-21

Examining board members

Márcia Cristina Anderson Braz Federson; Andréa Cristina Prokopczyk Arita; Pierluigi Benevieri; Miguel Vinicius Santini Frasson; Suzinei Aparecida Siqueira Marconato

• Advisor: Márcia Cristina Anderson Braz Federson

Abstract

The purpose of this work is to study some properties of solutions of generalized ordinary dierential equations and apply these results to some classical dierential equations (abstract ordinary dierential equations and measure functional dierential equations). The main results concern existence-uniqueness of a solution for a class of generalized ordinary dierential equations, continuous dependence of solutions with respect to initial conditions and basin of attraction. These results are transfered to a class of abstract ordinary dierential equations. We also obtain some results on the stability of the trivial solution of generalized ordinary dierential equations and we transfer these results to a class of measure functional dierential equations (AU)

• FAPESP's process: 09/06259-0 - Atractors for generalized ordinary differential equations and applications to functional differential equations
• Grantee: Eduard Toon
• Support Opportunities: Scholarships in Brazil - Doctorate