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Differential topology and topological methods for the study of differential equations on manifolds

Grant number: 16/19227-3
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): December 01, 2016
Effective date (End): November 30, 2017
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Pierluigi Benevieri
Grantee:Rodrigo Lima Dias
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The project deals with the study of the basic concepts in differential topology and their connections with the classical topological methods in nonlinear analysis, as the topological degree theory and the notion of degree of a tangent vector field to a differentiable manifold. These methods will be applied to the study of some differential equations, of first and second order, on manifolds. Classical topological results, as Brouwer and Schauder fixed point theorems will be tackled. (AU)

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