周期摄动保守系统周期解的存在唯一性(英文)

Existence and Uniqueness of Solution for Periodically Perturbed Conservative Systems

长期以来,许多学者对牛顿运动方程解的存在和唯一性问题进行过研究,解决这类问题的方法主要有不动点定理,扰动理论、全局反函数定理、连续同伦法、变分法等.引入非负强制函数,利用吸引盆理论和比较定理证明了周期摄动保守系统周期解存在的一个充分条件,并证明已有的一些结论是本文主要定理的推论.

For a long time,many authors had studied the existence and uniqueness of solution of the Newtonian equations.There are some main methods to solve this kind of problem,for example,fixed point theorem,perturbation theory,the global inverse function theorem,homotopy method,variational method etc.In this paper,a new sufficient condition of the existence and uniqueness of periodic solution to periodically perturbed conservative systems is given by using the basin of attraction and comparison theorem.The result of this paper generalizes some existence theorem.