On The Existence Of Positive Periodic Solutions For A Nonlinear Systems Of Second-order Ordinary Differential Equations

In this paper, we consider the existence of positive periodic solutions for a system of second-order nonlinear differential equations, in which the nonlinear term is sublinear in one equation and superlinear in the other equation. By constructing the Cartesian product of two cones in C[0,1], and using the fixed point theorem of cone expansion and compression, we obtain the existence of positive solutions of the system.