一类非线性微分方程组中心和焦点判定的简便方法  

Simple Criterion for the Center and Focus of a Class of Nonlinear Differential Equations

作　　者：张全信[1] 

机构地区：[1]滨州师范专科学校,山东256604

出　　处：《数学的实践与认识》2001年第3期357-359,共3页Mathematics in Practice and Theory

摘　　要：本文讨论非线性微分方程组dxdt=-y +x F( x,y) ,dydt=x +y F( x,y)( 1 )在奇点 ( 0 ,0 )邻近积分曲线的结构 .得到了判定原点 ( 0 ,0 )是微分方程组 ( 1 )的焦点或中心的简便方法 .The structure of the orbits of a class of nonlinear differential equations near the origin is discussed, and gets the two new theorems with which we can decide that the originis the focus or center of the differential equations.

关 键 词：非线性 微分方程 积分曲线 焦点 中心 特征根 

分 类 号：O175[理学—数学]