The Qualitative Theory of Ordinary Differential Equations and Introduction to Impulsive Differential Equations

• Grant number: 10/05897-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2010
• End date: June 30, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Suzinei Aparecida Siqueira Marconato
• Grantee: Glalco Silva Costa
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

The project aims to establish the qualitative theory of ordinary differential equations (ODE) and introduce the concepts and basic results on impulsive differential equations (IDE). That is, state and prove the classical results on existence of solution, continuation of solution continuation with respect to initial conditions and study the stability of systems of ordinary differential equations. Illustrate this theory through biological models and / or ecological prey-predator type. Introduce the concept of impulse by Model-Kruger Thiemer that describes how a drug is absorbed by the body. Study results that guarantee the existence of solution to a problem involving an ordinary differential equation and a further condition of impulse and finally establish the contrasts between EDO and EDI.