JournalszaaVol. 28 , No. 4DOI 10.4171/zaa/1393

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

  • Pierluigi Benevieri

    Universita di Firenze, Italy
  • Massimo Furi

    Università di Firenze, Italy
  • Maria Patrizia Pera

    Universita di Firenze, Italy
  • Alessandro Calamai

    Università Politecnica delle Marche, Ancona, Italy
Delay Differential Equations on Manifolds and Applications to Motion Problems for Forced Constrained Systems cover

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.