SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research

Global continuation of periodic solutions for retarded functional differential equations on manifolds

Pierluigi Benevieri12, Alessandro Calamai3, Massimo Furi1 and Maria Patrizia Pera1*

Author Affiliations

1 Dipartimento di Matematica e Informatica, Università degli Studi di Firenze, Via S. Marta 3, Firenze, I-50139, Italy

2 Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, São Paulo, 05508-090, Brasil

3 Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, Ancona, I-60131, Italy

For all author emails, please log on.

Boundary Value Problems 2013, 2013:21  doi:10.1186/1687-2770-2013-21

Published: 11 February 2013

Abstract

We consider T-periodic parametrized retarded functional differential equations, with infinite delay, on (possibly) noncompact manifolds. Using a topological approach, based on the notions of degree of a tangent vector field and of the fixed point index, we prove a global continuation result for T-periodic solutions of such equations.

Our main theorem is a generalization to the case of retarded equations of a global continuation result obtained by the last two authors for ordinary differential equations on manifolds. As corollaries we obtain a Rabinowitz-type global bifurcation result and a continuation principle of Mawhin type.

MSC: 34K13, 34C40, 37C25, 70K42.

Keywords:
retarded functional differential equations; global bifurcation; fixed point index; degree of a vector field