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) + lambda b(t)f(u(t - tau(t))), t is an element of R by using global bifurcation techniques. Where a, b is an element of C(R, [0, infinity)) are omega-periodic functions with integral(omega)(0) a(t)dt > 0, integral(omega)(0) b(t)dt > 0, tau is a continuous omega-periodic function, and lambda > 0 is a parameter. f is an element of C (R, R) and there exist two constants s(2) < 0 < s(1) such that f(s(2)) = f(0) = f(s(1)) = 0, f(s) > 0 for s is an element of (0, s(1)) boolean OR (s(1), infinity) and f(s) < 0 for s is an element of (-infinity, s(2)) boolean OR (s(2), 0).