Functional differential equations with state-dependent delay

• Grant number: 22/04392-0
• Support Opportunities: Scholarships in Brazil - Master
• Start date: September 01, 2022
• End date: February 29, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Eduardo Alex Hernández Morales
• Grantee: Edmara Viana da Silva
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

The objective of this project is give to the student a good background on functional differential equations by mean of the study of some differential problems on neutral differential equations with state dependent delay. In addition to the different disciplines of our master-program in mathematics and some specifical disciplines on functional differential equations, the project consider the study of the research papers1. Grimm, L. J.Existence and continuous dependence for a class of nonlinear neutral-differential equations. Proc. Amer. Math. Soc. 29 (1971), 467-473,2. Hernandez, Eduardo., On explicit abstract neutral differential equations with state-dependent delay. Submitted for publication,concerning neutral functional differential equations with state dependent delay. Concerning the above works, the basic objective is the study of the results about the local and global existence os solutions, the uniqueness of solutions and the the well-posedness of the problems studied in the cited works.The first work is a pioneer work on differential equations with state dependent arguments and the study of this work is a useful manner to begin the study of this type of functional differential problems. The second work is a recent an non-trivial work and the motivation for the review of this work is to create real academic conditions for PHd-studies in the field of functional differential equations wih state-dependent delay.The develop of the project complement strongly the academical background of the student in real analysis, function analysis and differential equations and is a first step for doctoral studies and research activities in the field of functional differential equations.

Academic Publications

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

SILVA, Edmara Viana da. Functional differential equations with state-dependent delay. 2024. Master's Dissertation - Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (PCARP/BC) Ribeirão Preto.