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

Abstract

We study one-signed periodic solutions of the first-order functional differential equationu'(t)=-a(t)u(t)+λb(t)f(u(t-τ(t))),t∈Rby using global bifurcation techniques. Wherea,b∈C(R,[0,∞))areω-periodic functions with∫0ωa(t)dt>0,∫0ωb(t)dt>0,τis a continuousω-periodic function, andλ>0is a parameter.f∈C(R,R)and there exist two constantss2<0<s1such thatf(s2)=f(0)=f(s1)=0,f(s)>0fors∈(0,s1)∪(s1,∞)andf(s)<0fors∈(-∞,s2)∪(s2,0).