One-Signed Periodic Solutions of First-Order Functional Differential Equations with a Parameter

We study one-signed periodic solutions of the first-order functional differential equation u'(t)=-a(t)u(t)+λb(t)f(u(t-τ(t))), t∈R by using global bifurcation techniques. Where a,b∈C(R,[0,∞)) are ω-periodic functions with ∫0ωa(t)dt>0, ∫0ωb(t)dt>0, τ is a continuous ω-periodic function, and λ>0 is a parameter. f∈C(R,R) and there exist two constants s2<00 for s∈(0,s1)∪(s1,∞) and f(s)<0 for s∈(-∞,s2)∪(s2,0)