| 不动点理论与里卡提方程两个正周期解的存在性 |
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| 引用本文： | 倪,华.不动点理论与里卡提方程两个正周期解的存在性[J].应用数学,2021,34(2):385-396. |
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| 作者姓名： | 倪 华 |
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| 作者单位： | 江苏大学数学科学学院, 江苏 镇江 212013 |
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| 基金项目： | Supported by the Special Project Supported by Senior Personnel of Jiangsu University(14JDG176)。 |
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| 摘 要： | 利用压缩映射原理,得到里卡提方程一个正周期解的存在性;利用变量变换方法,将里卡提方程转化为伯努利方程.根据伯努利方程的周期解和变量变换,得到里卡提方程的另一个周期解.并讨论了两个正周期解的稳定性,一个周期解在某个区间上是吸引的,另一个周期解在R上是不稳定的.
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| 关 键 词： | 里卡提方程 压缩映射 周期解 稳定性 |
| 收稿时间： | 2020/4/25 0:00:00 |
Fixed Point Theory and the Existence of Two Positive Periodic Solutions of Riccati's Equation |
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| NI Hua.Fixed Point Theory and the Existence of Two Positive Periodic Solutions of Riccati's Equation[J].Mathematica Applicata,2021,34(2):385-396. |
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| Authors: | NI Hua |
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| Institution: | (School of Mathematical Science,Jiangsu University,Zhenjiang 212013,China) |
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| Abstract: | This paper deals with a class of Riccati’s equation.By the principle of contraction mapping,the existence of one positive periodic solution of Riccati’s equation is obtained;By variable transformation method,Riccati’s equation is turned into Bonulli’s equation.According to the periodic solution of Bernoulli’s equation and variable transformation,another periodic solution of Riccati’s equation is obtained.And we discuss the stability of the two positive periodic solutions,one periodic solution is attractive on some region and unstable on another region,and another periodic solution is unstable on R. |
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| Keywords: | Riccati’s equation Contraction mapping Periodic solution Stability |
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