Existence and bifurcation of solutions of some nonlinear differential equations: a topological approach

• Grant number: 10/20727-4
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2011
• End date: May 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Pierluigi Benevieri
• Grantee: Pierluigi Benevieri
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The purpose is the study of some problems of nonlinear delay and ordinary differential equations, in order to obtain results of existence and bifurcation of solutions. The approch will be topological by means, in particular, of the topological degree e the fixed point index theory. In the topological approach a differential equation is associated to an equivalent functional equation between suitable function spaces (of infinite dimension). In many cases are involved Fredholm operators of index zero. Therefore, another purpose of the project will be the investigation of some topics in the topology of Fredholm operators, as the orientation (in infinite dimension), the topological degree for nonlinear Fredholm maps between Banach spaces, the spectral flow of continuous paths of self adjoint Fredholm operators in Hilbert spaces. (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. ON THE DEGREE FOR ORIENTED QUASI-FREDHOLM MAPS: ITS UNIQUENESS AND ITS EFFECTIVE EXTENSION OF THE LERAY-SCHAUDER DEGREE. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 46, n. 1, p. 401-430, SEP 2015. (10/20727-4)