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

In this paper, we consider the existence andmultiplicity of positive periodic solutions for first-order vector differential equation x (t) + f (t,x(t)) = 0, a.e. t ∈ [0,ω] under the periodic boundary value condition x(0) = x(ω). Here ω is a positive constant, and f : [0,ω] × Rn →Rn is a Carathéodory function. Some existence and multiplicity results of positive periodic solutions are derived by using a fixed point theorem in cones. © 2006 Elsevier Inc. All rights reserved.