| 1. | On the growth of solutions of second order linear non - homogeneous differential equations
二阶线性非齐次微分方程解的增长性 |
| 2. | An integrable theorem of second order linear non - homogeneous differential equation
一类二阶变系数线性微分方程的积分因子解法 |
| 3. | An integrable theorem of second order linear homogeneous differential equation
二阶线性常系数非齐次常微分方程的分解式讲授方法 |
| 4. | Conditions of linear homogeneous differential equation system with constant coefficients has non - zero solution
常系数齐次线性微分方程组有非零解的条件 |
| 5. | On the growth of solutions of second order non - homogeneous differential equations with meromorphic coefficients
二阶亚纯函数系数的非齐次微分方程解的增长性 |
| 6. | On the zero and hype - order of solutions of certain non - homogeneous differential equations with entire coefficients
关于某类缺项级数系数非齐次线性微分方程解的增长性 |
| 7. | On the numerical solution of the cauchy problem for ordinary linear homogeneous differential equations on large intervals of integration
齐次线性常微分方程组柯西问题在大积分区间上的数值解 |
| 8. | The similar structure of solution of second - order linear homogeneous differential equation with constant coefficients on the boundary value problem
二阶常系数齐次线性微分方程边值问题的解的相似结构 |
| 9. | In chapter 2 , we study the regularity of solutions of some second order differential equations . in chapter 3 , we study the regularity of solutions of higher order non - homogeneous differential equations where coefficients are rational functions or super entire functions . in chapter 4 , we study the regularity of solutions of higher order homogeneous differential equations where coefficients are super meromorphic functions
其中第二章研究了某些二阶方程解的正规性；第三章在系数分别为有理函数和超越整函数的情况下研究了高阶非齐次方程解的正规性；第四章在系数为超越亚纯函数的情况下研究了高阶齐次方程解的正规性；第五章则是假设在方程系数为正规亚纯函数的条件下得到的解的增长性方面的结果。 |
| 10. | In the second section of chapter 2 , the fact that the essential interest rates of all nodes differ from each other is discussed , a non - homogeneous differential equation model of interest rate - amount of circulating fund is established , and it is proved that the sum of the weighted interest rates of each node in the financial network still remains a constant and that the difference of the instant interest rates between two nodes will finally approach the difference between their basic interest rates . in the third section of chapter 2 , the differential equation model of interest rate - amount of circulating fund in an open system is studied , the laws of changes of interest rate are taken into account when fund is injected into or withdrawn from the node or when fund is injected into the network or withdrawn from the network , and the stability of equilibrium solution is proved based upon lyapunov stability theory . in the last , the equation model of interest rate - amount of circulating fund in the financial network with time delay is studied , and a necessary and sufficient condition for the existence of periodic solution is obtained to the interest rate - amount of circulating fund equation with delay
本文第二章首先建立了封闭系统的利率?流通量微分方程模型，证明了各结点利率加权和为常数即金融市场利率均衡原理，以及各结点利率极限为整个网络平均利率；其次在各结点基本利率不相同的情况下，建立了非齐次利率?流通量微分方程模型，证明了金融网络各结点利率加权和仍是一个常数，并证明了各结点两两之间的即时利率之差最终将稳定地趋于其基本利率差；此外，还研究了开放金融网络利率?流通量方程模型，考虑了结点自身追加资金和提走资金的情形以及网络外部注入资金和向外部转移资金情形下的利率变化规律，用lyapunov稳定性理论证明了模型均衡解的稳定性；最后，还研究了具有时滞的金融网络利率?流通量方程模型，并给出了具有时滞金融网络的利率流通量方程具有周期解的充要条件。 |
