The connections between the Kronecker index and the Leray-Schauder degree in the topological degree theory

• Grant number: 22/14913-7
• Support Opportunities: Scholarships abroad - Research
• Start date: January 23, 2023
• End date: July 22, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Pierluigi Benevieri
• Grantee: Pierluigi Benevieri
• Host Investigator: Maria Patrizia Pera
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Università degli Studi di Firenze, Italy

Abstract

The Leray-Schauder degree is a topological tool with numerous applications in pure mathematics and applied science problems. Many problems have, as a natural environment, infinite-dimensional differentiable manifolds, which can be particular metric spaces of functions. The theory lacks a relationship between the topological degree between infinite-dimensional manifolds and tools like the finite-dimensional Brouwer degree. In our research, we want to obtain results that can fill this gap. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BENEVIERI, PIERLUIGI; CALAMAI, ALESSANDRO; FURI, MASSIMO; PERA, MARIA PATRIZIA. An infinite dimensional version of the intermediate value theorem. Journal of Fixed Point Theory and Applications, v. 25, n. 3, p. 25-pg., 2023-09-01. (22/14913-7)