Periodic Perturbations With Delay of Autonomous Differential Equations on Manifolds
Massimo Furi, Marco Spadini · Advanced Nonlinear Studies · 2009
Abstract We apply topological methods to the study of the set of harmonic solutions of periodically perturbed autonomous ordinary differential equations on differentiable manifolds, allowing the perturbing term to contain a fixed delay. In the crucial step, in order to cope with the delay, we define a suitable (infinite dimensional) notion of Poincaré T-translation operator and prove a formula that, in the unperturbed case, allows the computation of its fixed point index.