Abstract and Applied Analysis
Volume 2011 (2011), Article ID 843292, 11 pages
Research Article

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

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 8 June 2011; Accepted 29 August 2011

Academic Editor: Ferhan M. Atici

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.


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))), tR by using global bifurcation techniques. Where a,bC(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. fC(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).