Higher order averaging theory for finding periodic solutions via Brouwer degree

Author(s)

Llibre, Jaume ^[1] ; Novaes, Douglas D. ^{[1, 2]} ; Teixeira, Marco A. ^[2]

Affiliation

^[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain

^[2] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Nonlinearity; v. 27, n. 3, p. 563-583, MAR 2014.
• Web of Science Citations: 36

Abstract

In this paper we deal with nonlinear differential systems of the form x'(t) = Sigma(k)(i=0) epsilon(i) F(i()t,x) + epsilon(k+1) R(t,x,epsilon), where F-i : R x D -> R-n for i = 0, 1, ... , k, and R : R x D x (-epsilon 0, epsilon 0). R-n are continuous functions, and T - periodic in the first variable, D being an open subset of R-n, and epsilon a small parameter. For such differential systems, which do not need to be of class C-1, under convenient assumptions we extend the averaging theory for computing their periodic solutions to k-th order in epsilon. Some applications are also performed. (AU)

• FAPESP's process: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems
• Grantee: Marco Antônio Teixeira
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 13/16492-0 - Averaging Theory for studying the periodic solutions of the differential systems and its applications
• Grantee: Douglas Duarte Novaes
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate