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.
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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. 451–474DOI 10.4171/ZAA/1393