Multiple solutions for periodic perturbations of a delayed autonomous system near an equilibrium

Abstract

Small non-autonomous perturbations around an equilibrium of a nonlinear delayed system are studied. Under appropriate assumptions, it is shown that the number of T-periodic solutions lying inside a bounded domain Ω ⊂ R N is, generically, at least |χ ± 1| + 1, where χ denotes the Euler characteristic of Ω. Moreover, some connections between the associated fixed point operator and the Poincaré operator are explored.