复系数Riccati微分方程解的存在条件及应用  

The Existence Condition and Application of the Solution of Riccati Differential Equation with Complex Coefficient

作　　者：王明建[1] 胡博[2] 王桂花[1] 

机构地区：[1]郑州师范学院数学与统计学院,郑州450044 [2]河南工业大学理学院,郑州450002

出　　处：《西安文理学院学报（自然科学版）》2016年第3期34-36,共3页Journal of Xi’an University(Natural Science Edition)

基　　金：国家自然科学基金项目(11161018)

摘　　要：对于系数是复常数的Riccati微分方程,y'=py2+qy+r,其中p=a+bi,q=c+di,r=e+f i是复数,a,b,c,d,e,f∈R,i是虚单位,且pr≠0,得到了此类方程解存在的一些条件,并给出了相关的应用.In this paper, for the Riccati differential equation of y＇ = py2 ＋ qy ＋ r with complex coefficient, among them p = a ＋ bi,q = c ＋ di and r = e ＋fi are complex numbers, a, b,c,d, e, f∈ R,i is a virtual unit and pr≠0. Some conditions for the existence of solutions of these equa- tions are obtained, and the related applications are given.

关 键 词：复常数 RICCATI微分方程 解存在条件 应用 

分 类 号：O175.5[理学—数学]