Topological methods in the study of periodic solutions of non-smooth differential equations

• Grant number: 18/22689-4
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: April 01, 2019
• End date: March 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Douglas Duarte Novaes
• Grantee: Francisco Bruno Gomes da Silva
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 22/04184-8 - Averaging theory for finding periodic solutions of Carathéodory differential equations via topological degree theory, BE.EP.DR

Abstract

The main objective of this project consists in the study of limit cycles of continuous differential equations by means of topological tools such as the Brouwer degree and the coincidence degree. The theme of this project is strongly based on recent publications which generalize, for non-smooth differential equations, some classical techniques (Averaging Theory and Melnikov's Method) used in the study of the persistence of periodic solutions for, until latelly, sufficiently smooth differential equations. Such publications represent a considerable advance in the theory of bifurcation of limit cycles. In this project we will study these works as well as the topological methods used thereof and also generalize the results aforementioned for non-Lipschitzian systems. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

NOVAES, DOUGLAS D.; SILVA, FRANCISCO B.. HIGHER ORDER ANALYSIS ON THE EXISTENCE OF PERIODIC SOLUTIONS IN CONTINUOUS DIFFERENTIAL EQUATIONS VIA DEGREE THEORY. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v. 53, n. 2, p. 15-pg., 2021-01-01. (19/10269-3, 18/22689-4, 18/16430-8, 18/13481-0)

Academic Publications

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

SILVA, Francisco Bruno Gomes da. Métodos topológicos no estudo de soluções periódicas de equações diferenciais não-suaves. 2024. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.