A Note on Periodic Solutions of Second Order Nonautonomous Singular Coupled Systems

Some classical tools have been used in the literature to study the positive solutions for twopoint boundary value problems of a coupled system of differential equations. These classical tools include some fixed point theorems in cones for completely continuous operators and Leray-Schauder fixed point theorem; for examples, see 1–3 and literatures therein. Recently, Schauder’s fixed point theorem has been used to study the existence of positive solutions of periodic boundary value problems in several papers; see, for example, Torres 4 , Chu et al. 5, 6 , Cao and Jiang 7 , and the references contained therein. However, there are few works on periodic solutions of second-order nonautonomous singular coupled systems. In these papers above, there are the major assumption that their associated Green’s functions are positive. Since Green’s functions are positive, in the paper, we continue to study the existence of periodic solutions to second-order nonautonomous singular coupled systems in the following form: