Copyright © 2011 Ruyun Ma and Yanqiong Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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<0<s1 such that f(s2)=f(0)=f(s1)=0, f(s)>0 for s∈(0,s1)∪(s1,∞) and f(s)<0 for s∈(-∞,s2)∪(s2,0).