Newton方程周期解存在性的构造性证明

A Constructive Proof on the Existence of Periodic Solution of Newton Equation

本文在条件n2≤α（t）≤gx（t，x）≤b（t）≤（n＋1）2下，构造性地证明了Newton方程x″（t）十g（t，x（t））＝0的2π－周期解的存在唯一性，证明过程同时提供了一种数值计算周期解的方法．

In this paper, under the conditionn2≤α(t) ≤gx(t) ≤ b(t)≤(n +1 )2, a constructive proof on the existence and uniqueness of 2π-periodic solution of Newton equation is given. Meanwhile.this approach provides a global method for finding solution of Newton equation.