含三个非线性项的三阶拟线性微分方程稳定性的新结果  

New results on the stability of third order quasilinear differential equation with three nonlinear terms

作　　者：阎承梓[1] 

机构地区：[1]华中师范大学数学与统计学学院,武汉430079

出　　处：《华中师范大学学报（自然科学版）》2011年第2期169-174,共6页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(10471052)

摘　　要：三阶拟线性微分方程(?)+f((?))+g((?))+h(x)=0解的稳定性是一个很典型的问题.人们针对其含有一个、两个、或三个非线性项的情形进行了广泛的研究,得出了许多有用的结果.本文应用李雅普洛夫函数方法讨论含三个非线性项的三阶拟线性微分方程解的稳定性,得到了此类方程解的稳定性的若干新结果.The stability of the solution of the third order quasilinear differential equation x＋f（x） ＋g（x）＋h （x）= 0 is a typical question. People have made extensive efforts in the study of this question with respect to the cases of containing one, two or three non- linear terms and have got many useful results. This paper, used the Liapunov function method to discuss the stability of the solution of the third order quasilinear differential equation with three nonlinear terms and obtained some new results on the stability of the solution of this kind of equation.

关 键 词：非线性系统 李雅普洛夫函数 稳定 渐近稳定 全局渐近稳定 

分 类 号：O175.13[理学—数学]