Existence of positive periodic solutions of nonlinear first-order delayed differential equations

We consider the existence of positive omega-periodic solutions for the equation u'(t) = a(t)g(u(t))u(t) - lambda b(t)f (u(t -tau(t))), 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; f, g is an element of C([0, infinity). [0, infinity)) and f (s) > 0 for s > 0; tau is a continuous omega-periodic function; lambda > 0 is a parameter. The proofs of our main results are based upon fixed point index theory. (C) 2011 Elsevier Inc. All rights reserved.