Periodic solutions for a system of the first order nonautonomous differential equations

Abstract

In this paper, we rigorously show the existence of multiple positive periodic solutions for a system of the first order nonautonomous differential equations in the form of { x ̇ = x F 1 ( t , x , y ) , y ̇ = y F 2 ( t , x , y ) . The proof relies on some analytical techniques and coincidence degree theory. As an application, we study two classes of biological population models, both of which have at least four positive periodic solutions.