The approach of Partial Differential Equations by tools from Modern Analysis.

• Grant number: 22/05728-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2022
• End date: February 29, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Adilson Eduardo Presoto
• Grantee: Carlos Eduardo Passarin Segantin
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

In order to approach Partial Differential Equations new areas in Mathematics have arisenand been expanded as Functional Analysis, Theory of Measure, Variational Calculus. Nowadaysthey are important tools to obtain existence, multiplicity and bifurcation results for PDEs.A combination of different approaches such as methods from Potential Theory, e.g. Perron'sMethod and Poincaré's Sweeping Method, Functional Analysis, e.g. Fredholm's Alternative andLax-Milgran Theorem and Variational Methods are employed throughout this project to studyPDEs. Advantages and limitations of each method are explored.