Multiple solutions for periodic perturbations of adelayed autonomous system near an equilibrium

GONZALO ROBLEDO; PABLO AMSTER; MARIEL PAULA KUNA

Congreso; XI Escuela Santaló 2019; 2019

In this work, we study small non-autonomous perturbations around anequilibrium of the following nonlinear delayed systemu0(t) = g(u(t), u(t − τ )) + p(t),where τ > 0, g : Ω × Ω → RN is continuously differentiable, p is continuousand T−periodic and Ω ⊂ RN .Under appropriate assumptions, it is shown that the number of T-periodicsolutions lying inside the bounded domain Ω is, generically, at least |χ ± 1|+1, where χ denotes the Euler characteristic of Ω.Moreover, some connections between the associated fixed point operatorand the Poincar´e operator are explored.