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

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Author(s):	Francisco Bruno Gomes da Silva Total Authors: 1
Document type:	Doctoral Thesis
Press:	Campinas, SP.
Institution:	Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
Defense date:	2024-04-09
Examining board members:	Douglas Duarte Novaes; Ricardo Miranda Martins; Ana Cristina de Oliveira Mereu; Murilo Rodolfo Cândido; Durval José Tonon
Advisor:	Douglas Duarte Novaes
Abstract
In this work a study of periodic solutions of non-smooth differential equations is carried out by means of the Averaging theory, the Brouwer degree and operator equations in Banach spaces. Sufficient conditions that ensure the persistence and convergence of periodic solutions of both non-Lipschitz continuous and Carathéodory discontinuous differential equations depending upon a small parameter are provided. The classical Melnikov and Averaging Theories for periodic smooth differential equations are presented as a way to motivate and expose the challenges of the study undertaken herein. The main results proved in this work are consistent with those already established in the literature and extend them to cases not yet covered, as it is properly evidenced with examples (AU)

FAPESP's process:	18/22689-4 - Topological methods in the study of periodic solutions of non-smooth differential equations
Grantee:	Francisco Bruno Gomes da Silva
Support Opportunities:	Scholarships in Brazil - Doctorate