关键词: 二阶常微分方程, 非线性导数项, 正2π-周期解, 闭凸锥, 不动点指数

Abstract: We discuss  the existence of positive 2π-periodic solutions of the second-order ordinary differential equation with nonlinear derivative term by using positive operator perturbation method and fixed point index theory in cones. Under certain inequality conditions of the 
nonlinear term f(t,x,y), we obtain the existence of positive 2π-periodic solutions of the equation.

Key words: second-order ordinary differential equation, nonlinear derivative term, positive 2π-periodic solution, closed convex cone, fixed point index