Fourth-Order Ordinary Differential Equations with Applications in Physics and Mechanics

• Grant number: 25/03040-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2025
• End date: April 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Ederson Moreira dos Santos
• Grantee: Arlen Tojal de Lucena
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 22/16407-1 - TESdE: Thematic on Equations and Systems of differential Equations, AP.TEM
• Associated scholarship(s): 25/21772-9 - Fourth order differential equations in suspension bridges models, BE.EP.IC

Abstract

This project aims to study a class of fourth-order ordinary differential equations that arise in modeling some problems from physics and mechanics, such as the study of traveling waves for the beam equation and certain models of bridge oscillations. The candidate will develop the skills to determine the existence and analyze the qualitative properties of special classes of solutions to these equations, including periodic, homoclinic, and heteroclinic solutions, thus contributing to his development as a researcher in the field of Analysis.