Delay Differential Equations on Manifolds and Applications to Motion Problems for Forced Constrained Systems
Pierluigi Benevieri
Universita di Firenze, ItalyMassimo Furi
Università di Firenze, ItalyMaria Patrizia Pera
Universita di Firenze, ItalyAlessandro Calamai
Università Politecnica delle Marche, Ancona, Italy

Abstract
We prove a global bifurcation result for T-periodic solutions of the delay T-periodic differential equation x'(t) = λf(t, x(t), x(t − 1)) on a smooth manifold (λ is a nonnegative parameter). The approach is based on the asymptotic fixed point index theory for _C_1 maps due to Eells–Fournier and Nussbaum. As an application, we prove the existence of forced oscillations of motion problems on topologically nontrivial compact constraints. The result is obtained under the assumption that the frictional coefficient is nonzero, and we conjecture that it is still true in the frictionless case.
Cite this article
Pierluigi Benevieri, Massimo Furi, Maria Patrizia Pera, Alessandro Calamai, Delay Differential Equations on Manifolds and Applications to Motion Problems for Forced Constrained Systems. Z. Anal. Anwend. 28 (2009), no. 4, pp. 451–474
DOI 10.4171/ZAA/1393