摘要
应用Mironenko建立的反射函数理论,给出了线性微分系统x.=A(t)x具有下三角型的反射矩阵的充要条件,同时建立了该线性微分系统为周期系统时的Poincaré映射,建立了该周期系统周期解的存在性和稳定性态的判定定理;另外,将有关线性微分系统的结论推广并应用到与其等价的非线性微分系统上,建立了该等价的非线性微分系统存在周期解的判定准则。
In the paper, we use the reflective function theory developed by Mironenko to establish the necessary and sufficient conditions for the existence of the lower triangle reflective matrix of the nlinear differential system . Meanwhile, the Poincare mapping is established when the nonlinear differential system is a periodic system and the decision theorem of the existence and stability of this system's periodic solutions is established as well. In addition, we spread and apply the relevant nlinear differential system's theories to the nonlinear differential system of equal values and establish the criterion to judge whether the nonlinear differential system of equal values has periodic solutions in the paper.
出处
《江南大学学报(自然科学版)》
CAS
2009年第2期245-249,共5页
Joural of Jiangnan University (Natural Science Edition)
关键词
微分系统
反射矩阵
周期解
differential system, reflective matrix, periodic solutions