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Averaging theory for finding periodic solutions of Carathéodory differential equations via topological degree theory

Grant number: 22/04184-8
Support Opportunities:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): August 01, 2022
Effective date (End): July 31, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Douglas Duarte Novaes
Grantee:Francisco Bruno Gomes da Silva
Supervisor: Armengol Gasull
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Research place: Universitat Autònoma de Barcelona (UAB), Spain  
Associated to the scholarship:18/22689-4 - Topological methods in the study of periodic solutions of non-smooth differential equations, BP.DR


Motivated by recent works generalizing the averaging theory for low regularity differential equations, this project proposes a higher order analysis for a family of perturbed Carathéodory differential equations aiming at finding sufficient conditions to guarantee the existence of periodic solutions of these equations that bifurcate from the non-perturbed system. It is also proposed to investigate how these periodic solutions converge as the perturbation parameter tends to zero. It is hoped that further ahead the results obtained in this research can be applied in problems of optimal control theory, where Carathéodory differential equations appear naturally. (AU)

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