一类周期系数微分方程的周期解

On Periodic Solutions of a Class of Differential Equation with Periodic Coefficients

利用所得引理，得到以下的系数为实连续周期函数的微分方程ｙ′＝ｆ（ｔ，ｙ）＝Ａ（ｔ）ｙｍ＋Ｂ（ｔ）ｙ＋ｃ（ｔ）（ｍ∈Ｎ，ｍ≥２）周期解的存在性和个数定理，同时给出了上面方程的周期解曲线与方程Ａ（ｔ）ｙｍ＋Ｂ（ｔ）ｙ＋ｃ（ｔ）＝０的实分枝曲线之间的关系．本文中的一些结果包含了以往文献中的相应结果．

Utilizing the derived theorem, the periodic solutions of the following differeatial equation with periodic coefficients are investigated.y′=f(t,y)=A(t)y m+B(t)y+c(t) (m∈N,m≥2)the theorems for existence and number are obtained. The relations between the real periodic solution curve of the above equation and the real branch curve of the equationA(t)y m+B(t)y+c(t)=0are also obtained. The results of this paper include the corresponding theorems in the past some works.