| 常微分方程解的存在唯一性定理的教学探索 |
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| 引用本文： | 王长有.常微分方程解的存在唯一性定理的教学探索[J].高师理科学刊,2011,31(2):89-92. |
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| 作者姓名： | 王长有 |
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| 作者单位： | 重庆邮电大学,数理学院,重庆,400065 |
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| 基金项目： | 重庆邮电大学重点课程建设项目 |
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| 摘 要： | 研究了一阶常微分方程的初值问题,通过构造上、下控制函数结合上、下解方法及不动点理论,证明了当非线性项连续时解的存在性,当非线性项Lipschitz连续时解的唯一性.该方法也适用于其它类型的微分方程研究.结合多年的教学与科研经验对"常微分方程解的存在唯一性定理"的课堂教学进行了分析与探讨.
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| 关 键 词： | 常微分方程 上、下解方法 不动点理论 |
Explore on the teaching of existence and uniqueness theorem for the solution of ordinary differential equation |
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| WANG Chang-you.Explore on the teaching of existence and uniqueness theorem for the solution of ordinary differential equation[J].Journal of Science of Teachers＇College and University,2011,31(2):89-92. |
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| Authors: | WANG Chang-you |
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| Institution: | WANG Chang-you(School of Mathematics and Physics,Chongqing University of Posts and Telecommunications,Chongqing 400065,China) |
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| Abstract: | The existence and uniqueness of solution for the ordinary differential equation was investigated by constructing the upper and lower control function and using the method of upper and lower solutions as well as fixed point theorem.It was shown that the initial value problem has a solution when the nonlinear term is continuous and has a unique solution when the nonlinear term is Lipschitz continuous.The method is the same with other type of differential equation.Moreover,the classroom teaching of the existen... |
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| Keywords: | ordinary differential equation upper and lower solution fixed-point theorem |
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