On periodic solutions of differential equations with delay and impulses

• Grant number: 08/00197-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: July 01, 2008
• End date: November 30, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Márcia Cristina Anderson Braz Federson
• Grantee: André Luiz Furtado
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The objective of this project is to investigate de dynamics defined by retarded functional differential equations (we write) RFDEs) with impulse action. We search for results on the existence and properties of periodic solutions to these equations. At first, we will study and establish conditions so that a certain RFDE which is subject to impulse effects admits a non-trivial periodic solution. Then we will consider a certain differential system which dos not have periodic solutions and we will look for conditions so that, under appropriate controls (impulses), the new system admits periodic solutions. Finallly, we will investigate the asymptotic stability of periodic solutions of impulsive RFDEs. One method we may employ to get the results is the theory of generalized ordinary differential equations and its techniques. a very general class of these equations admit a one-to-one correspondence with impulsive RFDEs. Another method we will use is the degree theory. We will consider differential-difference equations as well as differential equations with distributed delays. We are coing to consider pre-assigned moments of impulse effects where the applications accur mainly in pharmacokinetics, medicine, chemical technology, among others. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

FURTADO, André Luiz. On periodic solutions of retarded differential equations with impulses. 2012. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.