Generalized ordinary differential equations and their correspondences with other types of differential equations

• Grant number: 23/10170-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2023
• End date: September 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Suzete Maria Silva Afonso
• Grantee: Wellington Moisés de Oliveira
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

This project aims to explore the theory of generalized ordinary differential equations (generalized ODEs) and its correspondences with other types of differential equations, such as retarded functional differential equations, measure differential equations and impulsive differential equations. The main motivation to study the generalized ODEs is due to the fact that it is possible to obtain more general results concerning the qualitative properties of their solutions and translate them to the theories of the other types of equations that were mentioned through the established correspondences between them.