Existence Of Odd Periodic Solutions For A System Of Second-order Ordinary Differential Equations With Derivative Terms

Based on the Leray-Schauder fixed point theorem,Fourier analysis,fixed point index theorem on cone and the monotone iterative technique,we discuss the existence and uniqueness of odd 2π-periodic solutions for the second-order system of ordinary differential equations where f,g:R4→R are continuous function and 2π-periodic with respect to t.The main results are as follows:1.The existence and uniqueness of the odd 2π-periodic solutions for the system are obtained by applying Leray-Schauder fixed point theorem under the conditions that nonlinear terms f,g may be linear growth.2.The existence and uniqueness of odd 2π-periodic solutions for the system are obtained by applying the Leray-Schauder fixed point theorem and Fourier analysis method under the conditions that nonlinear terms f,g satisfy one-sided super-linear growth and Nagumo-type growth.3.The existence of the odd 2π-periodic solutions for the system are obtained under the conditions that the nonlinear terms f,g satisfy super-linear or sub-linear growth.4.The existence and uniqueness of the odd 2π-periodic solutions for the system are obtained by applying the monotone iterative technique under the conditions that nonlinear terms f,g satisfy Lipschitz type growth.