On the existence and multiplicity of positive periodic solutions for first-order vector differential equation

In this paper, we consider the existence and multiplicity of positive periodic solutions for first-order vector differential equation x'(t) + f (t, x (t)) = 0, a.e. t is an element of [0, omega] under the periodic boundary value condition x (0) = x (a)). Here a) is a positive constant, and f : [0, omega)] x R-n -> R-n is a Caratheodory function. Some existence and multiplicity results of positive periodic solutions are derived by using a fixed point theorem in cones. (c) 2006 Elsevier Inc. All rights reserved.