CAJ | 학술논문

为了研究多项式微分方程周期解的存在性与稳定性，通过多项式微分方程的广义反射函数来寻找其Poincaré映射。给出了多项式微分方程具有线性广义反射函数的充要条件，以及在该条件下线性广义反射函数的具体表达式和多项式微分方程周期解的存在性与稳定性。该结果对研究相关微分方程周期解与稳定性具有一定的参考价值和指导意义。
위료연구다항식미분방정주기해적존재성여은정성，통과다항식미분방정적엄의반사함수래심조기Poincaré영사。급출료다항식미분방정구유선성엄의반사함수적충요조건，이급재해조건하선성엄의반사함수적구체표체식화다항식미분방정주기해적존재성여은정성。해결과대연구상관미분방정주기해여은정성구유일정적삼고개치화지도의의。
In order to study the problem associated with periodic solution and stability of polyno-mial differential equation,this paper proposes a method to find its Poincarémapping through pol-ynomial differential equation’s generalized reflective function.It establishes the necessary and sufficient conditions for polynoe genermial differential equation to have linear generalized reflec-tive function.Under these conditions the form of thalized reflective function has been established and the existence and stability of the periodic solution has been discussed.This study is of refer-ence and guiding value for researches on the periodic solution and the stability of other differential equations.