摘要
1.问题的提出陈省身教授在中国科学院数学研究所讲学时,联系到空间曲线的封闭性问题,提出如下问题:周期系数的吕卡提方程在什么条件下存在周期解。即吕卡提(Riccati)方程dy/dx=A(x)y^(2)+B(x)y+C(x)(1.1)的系数A(x),B(x)及C(x)均为具有周期2π的实连续函数,方程(1.1)在什么条件下,具有周期2π的实连续解。
In this paper periodic solutions of Riccati’s equation with periodic coefficients are investigated.Both the necessary and sufficient conditions for existence and the criteria of stability are given.Equating the right side of Riccati’s equation to zero,we obtain an algebraic equation of degree 2,called"the characteristic equation".Close relations between periodic solutions of Riccati differential equation and those of its algebraic characteristic equation are established.
出处
《科学通报》
1979年第23期1062-1066,共5页
Chinese Science Bulletin
