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

Grant number: 10/05897-0
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): July 01, 2010
Effective date (End): June 30, 2011
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Suzinei Aparecida Siqueira Marconato
Grantee:Glalco Silva Costa
Home 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.

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