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

AbstractIn 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∈[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