Existence theorems of solutions for differential and integral equations

• Grant number: 13/11636-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2013
• End date: July 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Luis Antônio Fernandes de Oliveira
• Grantee: Saulo Portes dos Reis
• Host Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil

Abstract

The main of this scientific initiation work is to clarify to the student the importance of ensuring the existence of solutions of equations. Our choice was to discuss the topic through three cases that highlight similarities and differences between techniques. The gain from such an approach, in our opinion, allow the student transit through various concepts of General Topology and Functional Analysis and thus add notions and concepts that will be useful in the Master's / PhD in Mathematics.