nontrivial periodic solutions for delay differential systems via morse theory

the existence of the nontrivial periodic solutions to the system of delay differential equations

x′(t) = −f (x(t − τ )) (1.1)

is investigated, where x ∈ rⁿ , f ∈ c(rⁿ , rⁿ ). we prove several new existence results via morse theory and the galerkin methods.