Periodic and quasi periodic solution of functional dinamic differential equations on time scales

• Grant number: 11/22143-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2012
• End date: February 28, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Márcia Cristina Anderson Braz Federson
• Grantee: Clessius Silva
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Our aim is to investigate periodic and quasi periodic solutions of generalized ODEs by means of Lyapunov functionals. Then, using the correspondence between generalized ODEs and measure functional differential equations, we intend to extend the obtained results on periodic solutions to these equations. Besides, using the correspondence between measure functionals differential equations and impulsive functional differential equations on time scales, we intend to extend the results on periodic solution to these last equations. Also, we will investigate almost periodic solutions of generalized ODEs and we will apply the results to other type of equations described here. (AU)