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Zeitschrift für Analysis und ihre Anwendungen


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Volume 28, Issue 4, 2009, pp. 451–474
DOI: 10.4171/ZAA/1393

Published online: 2009-12-23

Delay Differential Equations on Manifolds and Applications to Motion Problems for Forced Constrained Systems

Pierluigi Benevieri[1], Alessandro Calamai[2], Massimo Furi[3] and Maria Patrizia Pera[4]

(1) Universita di Firenze, Italy
(2) Università Politecnica delle Marche, Ancona, Italy
(3) Università di Firenze, Italy
(4) Universita di Firenze, Italy

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 C1 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.

Keywords: Delay differential equations, periodic solutions, fixed point index theory, motion problems on manifolds

Benevieri Pierluigi, Calamai Alessandro, Furi Massimo, Pera Maria Patrizia: Delay Differential Equations on Manifolds and Applications to Motion Problems for Forced Constrained Systems. Z. Anal. Anwend. 28 (2009), 451-474. doi: 10.4171/ZAA/1393